Global Existence for the Einstein Vacuum Equations in Wave Coordinates View Full Text


Ontology type: schema:ScholarlyArticle     


Article Info

DATE

2005-05

AUTHORS

Hans Lindblad, Igor Rodnianski

ABSTRACT

We prove global stability of Minkowski space for the Einstein vacuum equations in harmonic (wave) coordinate gauge for the set of restricted data coinciding with the Schwarzschild solution in the neighborhood of space-like infinity. The result contradicts previous beliefs that wave coordinates are “unstable in the large” and provides an alternative approach to the stability problem originally solved ( for unrestricted data, in a different gauge and with a precise description of the asymptotic behavior at null infinity) by D. Christodoulou and S. Klainerman. Using the wave coordinate gauge we recast the Einstein equations as a system of quasilinear wave equations and, in absence of the classical null condition, establish a small data global existence result. In our previous work we introduced the notion of a weak null condition and showed that the Einstein equations in harmonic coordinates satisfy this condition.The result of this paper relies on this observation and combines it with the vector field method based on the symmetries of the standard Minkowski space. In a forthcoming paper we will address the question of stability of Minkowski space for the Einstein vacuum equations in wave coordinates for all “small” asymptotically flat data and the case of the Einstein equations coupled to a scalar field. More... »

PAGES

43-110

Identifiers

URI

http://scigraph.springernature.com/pub.10.1007/s00220-004-1281-6

DOI

http://dx.doi.org/10.1007/s00220-004-1281-6

DIMENSIONS

https://app.dimensions.ai/details/publication/pub.1047510537


Indexing Status Check whether this publication has been indexed by Scopus and Web Of Science using the SN Indexing Status Tool
Incoming Citations Browse incoming citations for this publication using opencitations.net

JSON-LD is the canonical representation for SciGraph data.

TIP: You can open this SciGraph record using an external JSON-LD service: JSON-LD Playground Google SDTT

[
  {
    "@context": "https://springernature.github.io/scigraph/jsonld/sgcontext.json", 
    "about": [
      {
        "id": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/0202", 
        "inDefinedTermSet": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/", 
        "name": "Atomic, Molecular, Nuclear, Particle and Plasma Physics", 
        "type": "DefinedTerm"
      }, 
      {
        "id": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/02", 
        "inDefinedTermSet": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/", 
        "name": "Physical Sciences", 
        "type": "DefinedTerm"
      }
    ], 
    "author": [
      {
        "affiliation": {
          "alternateName": "University of California, San Diego", 
          "id": "https://www.grid.ac/institutes/grid.266100.3", 
          "name": [
            "Mathematics Department, University of California at San Diego, 9500 Gilman Drive, 92093-0112, La Jolla, CA, USA"
          ], 
          "type": "Organization"
        }, 
        "familyName": "Lindblad", 
        "givenName": "Hans", 
        "id": "sg:person.01241765340.34", 
        "sameAs": [
          "https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.01241765340.34"
        ], 
        "type": "Person"
      }, 
      {
        "affiliation": {
          "alternateName": "Princeton University", 
          "id": "https://www.grid.ac/institutes/grid.16750.35", 
          "name": [
            "Department Mathematics, Fine Hall, Princeton University, 08544-1000, Princeton, NJ, USA"
          ], 
          "type": "Organization"
        }, 
        "familyName": "Rodnianski", 
        "givenName": "Igor", 
        "id": "sg:person.016520512675.36", 
        "sameAs": [
          "https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.016520512675.36"
        ], 
        "type": "Person"
      }
    ], 
    "citation": [
      {
        "id": "sg:pub.10.1007/bf01940959", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1000111119", 
          "https://doi.org/10.1007/bf01940959"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/bf01940959", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1000111119", 
          "https://doi.org/10.1007/bf01940959"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/bf01645389", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1001058818", 
          "https://doi.org/10.1007/bf01645389"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/bf01645389", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1001058818", 
          "https://doi.org/10.1007/bf01645389"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/bf01208277", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1002184326", 
          "https://doi.org/10.1007/bf01208277"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/bf01208277", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1002184326", 
          "https://doi.org/10.1007/bf01208277"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://app.dimensions.ai/details/publication/pub.1003723932", 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/978-1-4612-2084-8", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1003723932", 
          "https://doi.org/10.1007/978-1-4612-2084-8"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/978-1-4612-2084-8", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1003723932", 
          "https://doi.org/10.1007/978-1-4612-2084-8"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/978-1-4613-9136-4_6", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1003732706", 
          "https://doi.org/10.1007/978-1-4613-9136-4_6"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1002/cpa.3160450902", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1004232319"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1002/cpa.3160450902", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1004232319"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/bf02099131", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1015273331", 
          "https://doi.org/10.1007/bf02099131"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/bf02099131", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1015273331", 
          "https://doi.org/10.1007/bf02099131"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/bf02099131", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1015273331", 
          "https://doi.org/10.1007/bf02099131"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1016/s1631-073x(03)00231-0", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1021564457"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1016/s1631-073x(03)00231-0", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1021564457"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1088/0264-9381/20/14/319", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1022577520"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/bf01205488", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1024467877", 
          "https://doi.org/10.1007/bf01205488"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/bf01205488", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1024467877", 
          "https://doi.org/10.1007/bf01205488"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1002/cpa.3160390205", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1028949614"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1002/cpa.3160390205", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1028949614"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1002/cpa.3160370403", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1029232064"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1002/cpa.3160370403", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1029232064"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/s002220100165", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1038611174", 
          "https://doi.org/10.1007/s002220100165"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/bf02392131", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1043019855", 
          "https://doi.org/10.1007/bf02392131"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1002/cpa.3160430403", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1045698389"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1002/cpa.3160430403", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1045698389"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1002/(sici)1521-3889(200005)9:3/5<258::aid-andp258>3.0.co;2-y", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1047140935"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1002/(sici)1521-3889(200005)9:3/5<258::aid-andp258>3.0.co;2-y", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1047140935"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1002/cpa.3160340103", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1048874384"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1002/cpa.3160340103", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1048874384"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1088/0264-9381/19/9/101", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1050977677"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1002/cpa.3160380305", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1052958137"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1002/cpa.3160380305", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1052958137"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/bfb0077745", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1053001844", 
          "https://doi.org/10.1007/bfb0077745"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/pl00005533", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1053561726", 
          "https://doi.org/10.1007/pl00005533"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1142/9789812777386_0004", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1088781428"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1515/9781400863174", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1096908672"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1017/cbo9780511524646", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1098707667"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.7208/chicago/9780226870373.001.0001", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1099556543"
        ], 
        "type": "CreativeWork"
      }
    ], 
    "datePublished": "2005-05", 
    "datePublishedReg": "2005-05-01", 
    "description": "We prove global stability of Minkowski space for the Einstein vacuum equations in harmonic (wave) coordinate gauge for the set of restricted data coinciding with the Schwarzschild solution in the neighborhood of space-like infinity. The result contradicts previous beliefs that wave coordinates are \u201cunstable in the large\u201d and provides an alternative approach to the stability problem originally solved ( for unrestricted data, in a different gauge and with a precise description of the asymptotic behavior at null infinity) by D. Christodoulou and S. Klainerman. Using the wave coordinate gauge we recast the Einstein equations as a system of quasilinear wave equations and, in absence of the classical null condition, establish a small data global existence result. In our previous work we introduced the notion of a weak null condition and showed that the Einstein equations in harmonic coordinates satisfy this condition.The result of this paper relies on this observation and combines it with the vector field method based on the symmetries of the standard Minkowski space. In a forthcoming paper we will address the question of stability of Minkowski space for the Einstein vacuum equations in wave coordinates for all \u201csmall\u201d asymptotically flat data and the case of the Einstein equations coupled to a scalar field.", 
    "genre": "research_article", 
    "id": "sg:pub.10.1007/s00220-004-1281-6", 
    "inLanguage": [
      "en"
    ], 
    "isAccessibleForFree": false, 
    "isPartOf": [
      {
        "id": "sg:journal.1136216", 
        "issn": [
          "0010-3616", 
          "1432-0916"
        ], 
        "name": "Communications in Mathematical Physics", 
        "type": "Periodical"
      }, 
      {
        "issueNumber": "1", 
        "type": "PublicationIssue"
      }, 
      {
        "type": "PublicationVolume", 
        "volumeNumber": "256"
      }
    ], 
    "name": "Global Existence for the Einstein Vacuum Equations in Wave Coordinates", 
    "pagination": "43-110", 
    "productId": [
      {
        "name": "readcube_id", 
        "type": "PropertyValue", 
        "value": [
          "e252fe1e194a8b19517ec108b3258e2cde531fabccd4494cfd2c4f7a3e19fd70"
        ]
      }, 
      {
        "name": "doi", 
        "type": "PropertyValue", 
        "value": [
          "10.1007/s00220-004-1281-6"
        ]
      }, 
      {
        "name": "dimensions_id", 
        "type": "PropertyValue", 
        "value": [
          "pub.1047510537"
        ]
      }
    ], 
    "sameAs": [
      "https://doi.org/10.1007/s00220-004-1281-6", 
      "https://app.dimensions.ai/details/publication/pub.1047510537"
    ], 
    "sdDataset": "articles", 
    "sdDatePublished": "2019-04-11T14:28", 
    "sdLicense": "https://scigraph.springernature.com/explorer/license/", 
    "sdPublisher": {
      "name": "Springer Nature - SN SciGraph project", 
      "type": "Organization"
    }, 
    "sdSource": "s3://com-uberresearch-data-dimensions-target-20181106-alternative/cleanup/v134/2549eaecd7973599484d7c17b260dba0a4ecb94b/merge/v9/a6c9fde33151104705d4d7ff012ea9563521a3ce/jats-lookup/v90/0000000373_0000000373/records_13078_00000001.jsonl", 
    "type": "ScholarlyArticle", 
    "url": "http://link.springer.com/10.1007%2Fs00220-004-1281-6"
  }
]
 

Download the RDF metadata as:  json-ld nt turtle xml License info

HOW TO GET THIS DATA PROGRAMMATICALLY:

JSON-LD is a popular format for linked data which is fully compatible with JSON.

curl -H 'Accept: application/ld+json' 'https://scigraph.springernature.com/pub.10.1007/s00220-004-1281-6'

N-Triples is a line-based linked data format ideal for batch operations.

curl -H 'Accept: application/n-triples' 'https://scigraph.springernature.com/pub.10.1007/s00220-004-1281-6'

Turtle is a human-readable linked data format.

curl -H 'Accept: text/turtle' 'https://scigraph.springernature.com/pub.10.1007/s00220-004-1281-6'

RDF/XML is a standard XML format for linked data.

curl -H 'Accept: application/rdf+xml' 'https://scigraph.springernature.com/pub.10.1007/s00220-004-1281-6'


 

This table displays all metadata directly associated to this object as RDF triples.

159 TRIPLES      21 PREDICATES      53 URIs      19 LITERALS      7 BLANK NODES

Subject Predicate Object
1 sg:pub.10.1007/s00220-004-1281-6 schema:about anzsrc-for:02
2 anzsrc-for:0202
3 schema:author N1e16ab3530624584bf320b1504295dbc
4 schema:citation sg:pub.10.1007/978-1-4612-2084-8
5 sg:pub.10.1007/978-1-4613-9136-4_6
6 sg:pub.10.1007/bf01205488
7 sg:pub.10.1007/bf01208277
8 sg:pub.10.1007/bf01645389
9 sg:pub.10.1007/bf01940959
10 sg:pub.10.1007/bf02099131
11 sg:pub.10.1007/bf02392131
12 sg:pub.10.1007/bfb0077745
13 sg:pub.10.1007/pl00005533
14 sg:pub.10.1007/s002220100165
15 https://app.dimensions.ai/details/publication/pub.1003723932
16 https://doi.org/10.1002/(sici)1521-3889(200005)9:3/5<258::aid-andp258>3.0.co;2-y
17 https://doi.org/10.1002/cpa.3160340103
18 https://doi.org/10.1002/cpa.3160370403
19 https://doi.org/10.1002/cpa.3160380305
20 https://doi.org/10.1002/cpa.3160390205
21 https://doi.org/10.1002/cpa.3160430403
22 https://doi.org/10.1002/cpa.3160450902
23 https://doi.org/10.1016/s1631-073x(03)00231-0
24 https://doi.org/10.1017/cbo9780511524646
25 https://doi.org/10.1088/0264-9381/19/9/101
26 https://doi.org/10.1088/0264-9381/20/14/319
27 https://doi.org/10.1142/9789812777386_0004
28 https://doi.org/10.1515/9781400863174
29 https://doi.org/10.7208/chicago/9780226870373.001.0001
30 schema:datePublished 2005-05
31 schema:datePublishedReg 2005-05-01
32 schema:description We prove global stability of Minkowski space for the Einstein vacuum equations in harmonic (wave) coordinate gauge for the set of restricted data coinciding with the Schwarzschild solution in the neighborhood of space-like infinity. The result contradicts previous beliefs that wave coordinates are “unstable in the large” and provides an alternative approach to the stability problem originally solved ( for unrestricted data, in a different gauge and with a precise description of the asymptotic behavior at null infinity) by D. Christodoulou and S. Klainerman. Using the wave coordinate gauge we recast the Einstein equations as a system of quasilinear wave equations and, in absence of the classical null condition, establish a small data global existence result. In our previous work we introduced the notion of a weak null condition and showed that the Einstein equations in harmonic coordinates satisfy this condition.The result of this paper relies on this observation and combines it with the vector field method based on the symmetries of the standard Minkowski space. In a forthcoming paper we will address the question of stability of Minkowski space for the Einstein vacuum equations in wave coordinates for all “small” asymptotically flat data and the case of the Einstein equations coupled to a scalar field.
33 schema:genre research_article
34 schema:inLanguage en
35 schema:isAccessibleForFree false
36 schema:isPartOf N38118d2147064f0bae7f10265cdf2cb0
37 Ne954bd4b5ac541e6bc5f507226b7b09a
38 sg:journal.1136216
39 schema:name Global Existence for the Einstein Vacuum Equations in Wave Coordinates
40 schema:pagination 43-110
41 schema:productId N288faecf97cf4a05b08c29a7e766f131
42 N2d4d3531aedd406e9dd511e2c92aae82
43 Na0bf7f4e206449639a89e5a8da1904b9
44 schema:sameAs https://app.dimensions.ai/details/publication/pub.1047510537
45 https://doi.org/10.1007/s00220-004-1281-6
46 schema:sdDatePublished 2019-04-11T14:28
47 schema:sdLicense https://scigraph.springernature.com/explorer/license/
48 schema:sdPublisher N01fcf39111b44ca8a113cde6e1f17e5b
49 schema:url http://link.springer.com/10.1007%2Fs00220-004-1281-6
50 sgo:license sg:explorer/license/
51 sgo:sdDataset articles
52 rdf:type schema:ScholarlyArticle
53 N01fcf39111b44ca8a113cde6e1f17e5b schema:name Springer Nature - SN SciGraph project
54 rdf:type schema:Organization
55 N1e16ab3530624584bf320b1504295dbc rdf:first sg:person.01241765340.34
56 rdf:rest Nc17a94b4a9c542339753d067a9897845
57 N288faecf97cf4a05b08c29a7e766f131 schema:name doi
58 schema:value 10.1007/s00220-004-1281-6
59 rdf:type schema:PropertyValue
60 N2d4d3531aedd406e9dd511e2c92aae82 schema:name dimensions_id
61 schema:value pub.1047510537
62 rdf:type schema:PropertyValue
63 N38118d2147064f0bae7f10265cdf2cb0 schema:volumeNumber 256
64 rdf:type schema:PublicationVolume
65 Na0bf7f4e206449639a89e5a8da1904b9 schema:name readcube_id
66 schema:value e252fe1e194a8b19517ec108b3258e2cde531fabccd4494cfd2c4f7a3e19fd70
67 rdf:type schema:PropertyValue
68 Nc17a94b4a9c542339753d067a9897845 rdf:first sg:person.016520512675.36
69 rdf:rest rdf:nil
70 Ne954bd4b5ac541e6bc5f507226b7b09a schema:issueNumber 1
71 rdf:type schema:PublicationIssue
72 anzsrc-for:02 schema:inDefinedTermSet anzsrc-for:
73 schema:name Physical Sciences
74 rdf:type schema:DefinedTerm
75 anzsrc-for:0202 schema:inDefinedTermSet anzsrc-for:
76 schema:name Atomic, Molecular, Nuclear, Particle and Plasma Physics
77 rdf:type schema:DefinedTerm
78 sg:journal.1136216 schema:issn 0010-3616
79 1432-0916
80 schema:name Communications in Mathematical Physics
81 rdf:type schema:Periodical
82 sg:person.01241765340.34 schema:affiliation https://www.grid.ac/institutes/grid.266100.3
83 schema:familyName Lindblad
84 schema:givenName Hans
85 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.01241765340.34
86 rdf:type schema:Person
87 sg:person.016520512675.36 schema:affiliation https://www.grid.ac/institutes/grid.16750.35
88 schema:familyName Rodnianski
89 schema:givenName Igor
90 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.016520512675.36
91 rdf:type schema:Person
92 sg:pub.10.1007/978-1-4612-2084-8 schema:sameAs https://app.dimensions.ai/details/publication/pub.1003723932
93 https://doi.org/10.1007/978-1-4612-2084-8
94 rdf:type schema:CreativeWork
95 sg:pub.10.1007/978-1-4613-9136-4_6 schema:sameAs https://app.dimensions.ai/details/publication/pub.1003732706
96 https://doi.org/10.1007/978-1-4613-9136-4_6
97 rdf:type schema:CreativeWork
98 sg:pub.10.1007/bf01205488 schema:sameAs https://app.dimensions.ai/details/publication/pub.1024467877
99 https://doi.org/10.1007/bf01205488
100 rdf:type schema:CreativeWork
101 sg:pub.10.1007/bf01208277 schema:sameAs https://app.dimensions.ai/details/publication/pub.1002184326
102 https://doi.org/10.1007/bf01208277
103 rdf:type schema:CreativeWork
104 sg:pub.10.1007/bf01645389 schema:sameAs https://app.dimensions.ai/details/publication/pub.1001058818
105 https://doi.org/10.1007/bf01645389
106 rdf:type schema:CreativeWork
107 sg:pub.10.1007/bf01940959 schema:sameAs https://app.dimensions.ai/details/publication/pub.1000111119
108 https://doi.org/10.1007/bf01940959
109 rdf:type schema:CreativeWork
110 sg:pub.10.1007/bf02099131 schema:sameAs https://app.dimensions.ai/details/publication/pub.1015273331
111 https://doi.org/10.1007/bf02099131
112 rdf:type schema:CreativeWork
113 sg:pub.10.1007/bf02392131 schema:sameAs https://app.dimensions.ai/details/publication/pub.1043019855
114 https://doi.org/10.1007/bf02392131
115 rdf:type schema:CreativeWork
116 sg:pub.10.1007/bfb0077745 schema:sameAs https://app.dimensions.ai/details/publication/pub.1053001844
117 https://doi.org/10.1007/bfb0077745
118 rdf:type schema:CreativeWork
119 sg:pub.10.1007/pl00005533 schema:sameAs https://app.dimensions.ai/details/publication/pub.1053561726
120 https://doi.org/10.1007/pl00005533
121 rdf:type schema:CreativeWork
122 sg:pub.10.1007/s002220100165 schema:sameAs https://app.dimensions.ai/details/publication/pub.1038611174
123 https://doi.org/10.1007/s002220100165
124 rdf:type schema:CreativeWork
125 https://app.dimensions.ai/details/publication/pub.1003723932 schema:CreativeWork
126 https://doi.org/10.1002/(sici)1521-3889(200005)9:3/5<258::aid-andp258>3.0.co;2-y schema:sameAs https://app.dimensions.ai/details/publication/pub.1047140935
127 rdf:type schema:CreativeWork
128 https://doi.org/10.1002/cpa.3160340103 schema:sameAs https://app.dimensions.ai/details/publication/pub.1048874384
129 rdf:type schema:CreativeWork
130 https://doi.org/10.1002/cpa.3160370403 schema:sameAs https://app.dimensions.ai/details/publication/pub.1029232064
131 rdf:type schema:CreativeWork
132 https://doi.org/10.1002/cpa.3160380305 schema:sameAs https://app.dimensions.ai/details/publication/pub.1052958137
133 rdf:type schema:CreativeWork
134 https://doi.org/10.1002/cpa.3160390205 schema:sameAs https://app.dimensions.ai/details/publication/pub.1028949614
135 rdf:type schema:CreativeWork
136 https://doi.org/10.1002/cpa.3160430403 schema:sameAs https://app.dimensions.ai/details/publication/pub.1045698389
137 rdf:type schema:CreativeWork
138 https://doi.org/10.1002/cpa.3160450902 schema:sameAs https://app.dimensions.ai/details/publication/pub.1004232319
139 rdf:type schema:CreativeWork
140 https://doi.org/10.1016/s1631-073x(03)00231-0 schema:sameAs https://app.dimensions.ai/details/publication/pub.1021564457
141 rdf:type schema:CreativeWork
142 https://doi.org/10.1017/cbo9780511524646 schema:sameAs https://app.dimensions.ai/details/publication/pub.1098707667
143 rdf:type schema:CreativeWork
144 https://doi.org/10.1088/0264-9381/19/9/101 schema:sameAs https://app.dimensions.ai/details/publication/pub.1050977677
145 rdf:type schema:CreativeWork
146 https://doi.org/10.1088/0264-9381/20/14/319 schema:sameAs https://app.dimensions.ai/details/publication/pub.1022577520
147 rdf:type schema:CreativeWork
148 https://doi.org/10.1142/9789812777386_0004 schema:sameAs https://app.dimensions.ai/details/publication/pub.1088781428
149 rdf:type schema:CreativeWork
150 https://doi.org/10.1515/9781400863174 schema:sameAs https://app.dimensions.ai/details/publication/pub.1096908672
151 rdf:type schema:CreativeWork
152 https://doi.org/10.7208/chicago/9780226870373.001.0001 schema:sameAs https://app.dimensions.ai/details/publication/pub.1099556543
153 rdf:type schema:CreativeWork
154 https://www.grid.ac/institutes/grid.16750.35 schema:alternateName Princeton University
155 schema:name Department Mathematics, Fine Hall, Princeton University, 08544-1000, Princeton, NJ, USA
156 rdf:type schema:Organization
157 https://www.grid.ac/institutes/grid.266100.3 schema:alternateName University of California, San Diego
158 schema:name Mathematics Department, University of California at San Diego, 9500 Gilman Drive, 92093-0112, La Jolla, CA, USA
159 rdf:type schema:Organization
 




Preview window. Press ESC to close (or click here)


...