Optimal Maps and Exponentiation on Finite-Dimensional Spaces with Ricci Curvature Bounded from Below View Full Text


Ontology type: schema:ScholarlyArticle      Open Access: True


Article Info

DATE

2016-10

AUTHORS

Nicola Gigli, Tapio Rajala, Karl-Theodor Sturm

ABSTRACT

We prove existence and uniqueness of optimal maps on RCD∗(K,N) spaces under the assumption that the starting measure is absolutely continuous. We also discuss how this result naturally leads to the notion of exponentiation and to the local-to-global property of RCD∗(K,N) bounds.

PAGES

2914-2929

Identifiers

URI

http://scigraph.springernature.com/pub.10.1007/s12220-015-9654-y

DOI

http://dx.doi.org/10.1007/s12220-015-9654-y

DIMENSIONS

https://app.dimensions.ai/details/publication/pub.1040752965


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", 
    "author": [
      {
        "affiliation": {
          "alternateName": "International School for Advanced Studies", 
          "id": "https://www.grid.ac/institutes/grid.5970.b", 
          "name": [
            "University of Nice, Nice, France", 
            "SISSA, Trieste, Italy"
          ], 
          "type": "Organization"
        }, 
        "familyName": "Gigli", 
        "givenName": "Nicola", 
        "id": "sg:person.015012242515.20", 
        "sameAs": [
          "https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.015012242515.20"
        ], 
        "type": "Person"
      }, 
      {
        "affiliation": {
          "alternateName": "University of Jyv\u00e4skyl\u00e4", 
          "id": "https://www.grid.ac/institutes/grid.9681.6", 
          "name": [
            "University of Jyv\u00e4skyl\u00e4, Jyv\u00e4skyl\u00e4, Finland"
          ], 
          "type": "Organization"
        }, 
        "familyName": "Rajala", 
        "givenName": "Tapio", 
        "id": "sg:person.01166637667.10", 
        "sameAs": [
          "https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.01166637667.10"
        ], 
        "type": "Person"
      }, 
      {
        "affiliation": {
          "alternateName": "University of Bonn", 
          "id": "https://www.grid.ac/institutes/grid.10388.32", 
          "name": [
            "Universit\u00e4t Bonn, Bonn, Germany"
          ], 
          "type": "Organization"
        }, 
        "familyName": "Sturm", 
        "givenName": "Karl-Theodor", 
        "id": "sg:person.012150646646.44", 
        "sameAs": [
          "https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.012150646646.44"
        ], 
        "type": "Person"
      }
    ], 
    "citation": [
      {
        "id": "https://doi.org/10.1016/j.anihpc.2014.09.006", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1001980786"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1016/j.jfa.2010.03.024", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1004423076"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/s00222-013-0456-1", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1005998425", 
          "https://doi.org/10.1007/s00222-013-0456-1"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/s00526-011-0442-7", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1006224392", 
          "https://doi.org/10.1007/s00526-011-0442-7"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/s11511-006-0003-7", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1008600697", 
          "https://doi.org/10.1007/s11511-006-0003-7"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/s11511-006-0002-8", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1009828547", 
          "https://doi.org/10.1007/s11511-006-0002-8"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/978-3-540-34514-5", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1012306418", 
          "https://doi.org/10.1007/978-3-540-34514-5"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/978-3-540-34514-5", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1012306418", 
          "https://doi.org/10.1007/978-3-540-34514-5"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/pl00001679", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1012624304", 
          "https://doi.org/10.1007/pl00001679"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1090/s0002-9947-2015-06111-x", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1014856384"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/s12220-014-9537-7", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1027744448", 
          "https://doi.org/10.1007/s12220-014-9537-7"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1016/j.jfa.2012.02.015", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1028914334"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/978-3-642-32160-3_1", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1036211003", 
          "https://doi.org/10.1007/978-3-642-32160-3_1"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1016/j.jfa.2012.05.006", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1041981393"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/978-3-540-71050-9", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1043936119", 
          "https://doi.org/10.1007/978-3-540-71050-9"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/978-3-540-71050-9", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1043936119", 
          "https://doi.org/10.1007/978-3-540-71050-9"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/s00039-014-0255-x", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1045554281", 
          "https://doi.org/10.1007/s00039-014-0255-x"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/s00039-012-0176-5", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1045604700", 
          "https://doi.org/10.1007/s00039-012-0176-5"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/s00222-014-0563-7", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1051355220", 
          "https://doi.org/10.1007/s00222-014-0563-7"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1051/cocv/2010011", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1056951809"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1090/memo/1113", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1059344070"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1215/00127094-2681605", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1064411389"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.4007/annals.2009.169.903", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1071867138"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.4171/cmh/110", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1072316207"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.4310/maa.2011.v18.n2.a1", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1072461465"
        ], 
        "type": "CreativeWork"
      }
    ], 
    "datePublished": "2016-10", 
    "datePublishedReg": "2016-10-01", 
    "description": "We prove existence and uniqueness of optimal maps on RCD\u2217(K,N) spaces under the assumption that the starting measure is absolutely continuous. We also discuss how this result naturally leads to the notion of exponentiation and to the local-to-global property of RCD\u2217(K,N) bounds.", 
    "genre": "research_article", 
    "id": "sg:pub.10.1007/s12220-015-9654-y", 
    "inLanguage": [
      "en"
    ], 
    "isAccessibleForFree": true, 
    "isFundedItemOf": [
      {
        "id": "sg:grant.4246613", 
        "type": "MonetaryGrant"
      }
    ], 
    "isPartOf": [
      {
        "id": "sg:journal.1136350", 
        "issn": [
          "1050-6926", 
          "1559-002X"
        ], 
        "name": "The Journal of Geometric Analysis", 
        "type": "Periodical"
      }, 
      {
        "issueNumber": "4", 
        "type": "PublicationIssue"
      }, 
      {
        "type": "PublicationVolume", 
        "volumeNumber": "26"
      }
    ], 
    "name": "Optimal Maps and Exponentiation on Finite-Dimensional Spaces with Ricci Curvature Bounded from Below", 
    "pagination": "2914-2929", 
    "productId": [
      {
        "name": "readcube_id", 
        "type": "PropertyValue", 
        "value": [
          "c2215be9dd2b5cf60c2d194bd3a0a72101aa691cdc8f0e5bf7dafa3edb9c7a91"
        ]
      }, 
      {
        "name": "doi", 
        "type": "PropertyValue", 
        "value": [
          "10.1007/s12220-015-9654-y"
        ]
      }, 
      {
        "name": "dimensions_id", 
        "type": "PropertyValue", 
        "value": [
          "pub.1040752965"
        ]
      }
    ], 
    "sameAs": [
      "https://doi.org/10.1007/s12220-015-9654-y", 
      "https://app.dimensions.ai/details/publication/pub.1040752965"
    ], 
    "sdDataset": "articles", 
    "sdDatePublished": "2019-04-10T17:34", 
    "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/v90/0000000001_0000000264/records_8672_00000523.jsonl", 
    "type": "ScholarlyArticle", 
    "url": "http://link.springer.com/10.1007%2Fs12220-015-9654-y"
  }
]
 

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/s12220-015-9654-y'

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/s12220-015-9654-y'

Turtle is a human-readable linked data format.

curl -H 'Accept: text/turtle' 'https://scigraph.springernature.com/pub.10.1007/s12220-015-9654-y'

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

curl -H 'Accept: application/rdf+xml' 'https://scigraph.springernature.com/pub.10.1007/s12220-015-9654-y'


 

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

157 TRIPLES      20 PREDICATES      48 URIs      19 LITERALS      7 BLANK NODES

Subject Predicate Object
1 sg:pub.10.1007/s12220-015-9654-y schema:author N24ffc7ef45514d9fba9b14ed01b459ab
2 schema:citation sg:pub.10.1007/978-3-540-34514-5
3 sg:pub.10.1007/978-3-540-71050-9
4 sg:pub.10.1007/978-3-642-32160-3_1
5 sg:pub.10.1007/pl00001679
6 sg:pub.10.1007/s00039-012-0176-5
7 sg:pub.10.1007/s00039-014-0255-x
8 sg:pub.10.1007/s00222-013-0456-1
9 sg:pub.10.1007/s00222-014-0563-7
10 sg:pub.10.1007/s00526-011-0442-7
11 sg:pub.10.1007/s11511-006-0002-8
12 sg:pub.10.1007/s11511-006-0003-7
13 sg:pub.10.1007/s12220-014-9537-7
14 https://doi.org/10.1016/j.anihpc.2014.09.006
15 https://doi.org/10.1016/j.jfa.2010.03.024
16 https://doi.org/10.1016/j.jfa.2012.02.015
17 https://doi.org/10.1016/j.jfa.2012.05.006
18 https://doi.org/10.1051/cocv/2010011
19 https://doi.org/10.1090/memo/1113
20 https://doi.org/10.1090/s0002-9947-2015-06111-x
21 https://doi.org/10.1215/00127094-2681605
22 https://doi.org/10.4007/annals.2009.169.903
23 https://doi.org/10.4171/cmh/110
24 https://doi.org/10.4310/maa.2011.v18.n2.a1
25 schema:datePublished 2016-10
26 schema:datePublishedReg 2016-10-01
27 schema:description We prove existence and uniqueness of optimal maps on RCD∗(K,N) spaces under the assumption that the starting measure is absolutely continuous. We also discuss how this result naturally leads to the notion of exponentiation and to the local-to-global property of RCD∗(K,N) bounds.
28 schema:genre research_article
29 schema:inLanguage en
30 schema:isAccessibleForFree true
31 schema:isPartOf N24755e4bd8774531a43a09b241ce0363
32 Neba9f5eb2fdc441bac00564421452ccc
33 sg:journal.1136350
34 schema:name Optimal Maps and Exponentiation on Finite-Dimensional Spaces with Ricci Curvature Bounded from Below
35 schema:pagination 2914-2929
36 schema:productId N13c645ed921c493f93b2688fa44a9442
37 Neb6d89bbbdc349b2a53ae2f2fc593137
38 Nf8c15f50b01e43bf85c71c82d8611dd7
39 schema:sameAs https://app.dimensions.ai/details/publication/pub.1040752965
40 https://doi.org/10.1007/s12220-015-9654-y
41 schema:sdDatePublished 2019-04-10T17:34
42 schema:sdLicense https://scigraph.springernature.com/explorer/license/
43 schema:sdPublisher Necbad74f71544ecda2c16e69d7325d84
44 schema:url http://link.springer.com/10.1007%2Fs12220-015-9654-y
45 sgo:license sg:explorer/license/
46 sgo:sdDataset articles
47 rdf:type schema:ScholarlyArticle
48 N05a72811b365434f8c4c765298db2e18 rdf:first sg:person.012150646646.44
49 rdf:rest rdf:nil
50 N13c645ed921c493f93b2688fa44a9442 schema:name readcube_id
51 schema:value c2215be9dd2b5cf60c2d194bd3a0a72101aa691cdc8f0e5bf7dafa3edb9c7a91
52 rdf:type schema:PropertyValue
53 N24755e4bd8774531a43a09b241ce0363 schema:volumeNumber 26
54 rdf:type schema:PublicationVolume
55 N24ffc7ef45514d9fba9b14ed01b459ab rdf:first sg:person.015012242515.20
56 rdf:rest N8ae39f2e702a415d8cf9b7aa971aa21d
57 N8ae39f2e702a415d8cf9b7aa971aa21d rdf:first sg:person.01166637667.10
58 rdf:rest N05a72811b365434f8c4c765298db2e18
59 Neb6d89bbbdc349b2a53ae2f2fc593137 schema:name dimensions_id
60 schema:value pub.1040752965
61 rdf:type schema:PropertyValue
62 Neba9f5eb2fdc441bac00564421452ccc schema:issueNumber 4
63 rdf:type schema:PublicationIssue
64 Necbad74f71544ecda2c16e69d7325d84 schema:name Springer Nature - SN SciGraph project
65 rdf:type schema:Organization
66 Nf8c15f50b01e43bf85c71c82d8611dd7 schema:name doi
67 schema:value 10.1007/s12220-015-9654-y
68 rdf:type schema:PropertyValue
69 sg:grant.4246613 http://pending.schema.org/fundedItem sg:pub.10.1007/s12220-015-9654-y
70 rdf:type schema:MonetaryGrant
71 sg:journal.1136350 schema:issn 1050-6926
72 1559-002X
73 schema:name The Journal of Geometric Analysis
74 rdf:type schema:Periodical
75 sg:person.01166637667.10 schema:affiliation https://www.grid.ac/institutes/grid.9681.6
76 schema:familyName Rajala
77 schema:givenName Tapio
78 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.01166637667.10
79 rdf:type schema:Person
80 sg:person.012150646646.44 schema:affiliation https://www.grid.ac/institutes/grid.10388.32
81 schema:familyName Sturm
82 schema:givenName Karl-Theodor
83 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.012150646646.44
84 rdf:type schema:Person
85 sg:person.015012242515.20 schema:affiliation https://www.grid.ac/institutes/grid.5970.b
86 schema:familyName Gigli
87 schema:givenName Nicola
88 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.015012242515.20
89 rdf:type schema:Person
90 sg:pub.10.1007/978-3-540-34514-5 schema:sameAs https://app.dimensions.ai/details/publication/pub.1012306418
91 https://doi.org/10.1007/978-3-540-34514-5
92 rdf:type schema:CreativeWork
93 sg:pub.10.1007/978-3-540-71050-9 schema:sameAs https://app.dimensions.ai/details/publication/pub.1043936119
94 https://doi.org/10.1007/978-3-540-71050-9
95 rdf:type schema:CreativeWork
96 sg:pub.10.1007/978-3-642-32160-3_1 schema:sameAs https://app.dimensions.ai/details/publication/pub.1036211003
97 https://doi.org/10.1007/978-3-642-32160-3_1
98 rdf:type schema:CreativeWork
99 sg:pub.10.1007/pl00001679 schema:sameAs https://app.dimensions.ai/details/publication/pub.1012624304
100 https://doi.org/10.1007/pl00001679
101 rdf:type schema:CreativeWork
102 sg:pub.10.1007/s00039-012-0176-5 schema:sameAs https://app.dimensions.ai/details/publication/pub.1045604700
103 https://doi.org/10.1007/s00039-012-0176-5
104 rdf:type schema:CreativeWork
105 sg:pub.10.1007/s00039-014-0255-x schema:sameAs https://app.dimensions.ai/details/publication/pub.1045554281
106 https://doi.org/10.1007/s00039-014-0255-x
107 rdf:type schema:CreativeWork
108 sg:pub.10.1007/s00222-013-0456-1 schema:sameAs https://app.dimensions.ai/details/publication/pub.1005998425
109 https://doi.org/10.1007/s00222-013-0456-1
110 rdf:type schema:CreativeWork
111 sg:pub.10.1007/s00222-014-0563-7 schema:sameAs https://app.dimensions.ai/details/publication/pub.1051355220
112 https://doi.org/10.1007/s00222-014-0563-7
113 rdf:type schema:CreativeWork
114 sg:pub.10.1007/s00526-011-0442-7 schema:sameAs https://app.dimensions.ai/details/publication/pub.1006224392
115 https://doi.org/10.1007/s00526-011-0442-7
116 rdf:type schema:CreativeWork
117 sg:pub.10.1007/s11511-006-0002-8 schema:sameAs https://app.dimensions.ai/details/publication/pub.1009828547
118 https://doi.org/10.1007/s11511-006-0002-8
119 rdf:type schema:CreativeWork
120 sg:pub.10.1007/s11511-006-0003-7 schema:sameAs https://app.dimensions.ai/details/publication/pub.1008600697
121 https://doi.org/10.1007/s11511-006-0003-7
122 rdf:type schema:CreativeWork
123 sg:pub.10.1007/s12220-014-9537-7 schema:sameAs https://app.dimensions.ai/details/publication/pub.1027744448
124 https://doi.org/10.1007/s12220-014-9537-7
125 rdf:type schema:CreativeWork
126 https://doi.org/10.1016/j.anihpc.2014.09.006 schema:sameAs https://app.dimensions.ai/details/publication/pub.1001980786
127 rdf:type schema:CreativeWork
128 https://doi.org/10.1016/j.jfa.2010.03.024 schema:sameAs https://app.dimensions.ai/details/publication/pub.1004423076
129 rdf:type schema:CreativeWork
130 https://doi.org/10.1016/j.jfa.2012.02.015 schema:sameAs https://app.dimensions.ai/details/publication/pub.1028914334
131 rdf:type schema:CreativeWork
132 https://doi.org/10.1016/j.jfa.2012.05.006 schema:sameAs https://app.dimensions.ai/details/publication/pub.1041981393
133 rdf:type schema:CreativeWork
134 https://doi.org/10.1051/cocv/2010011 schema:sameAs https://app.dimensions.ai/details/publication/pub.1056951809
135 rdf:type schema:CreativeWork
136 https://doi.org/10.1090/memo/1113 schema:sameAs https://app.dimensions.ai/details/publication/pub.1059344070
137 rdf:type schema:CreativeWork
138 https://doi.org/10.1090/s0002-9947-2015-06111-x schema:sameAs https://app.dimensions.ai/details/publication/pub.1014856384
139 rdf:type schema:CreativeWork
140 https://doi.org/10.1215/00127094-2681605 schema:sameAs https://app.dimensions.ai/details/publication/pub.1064411389
141 rdf:type schema:CreativeWork
142 https://doi.org/10.4007/annals.2009.169.903 schema:sameAs https://app.dimensions.ai/details/publication/pub.1071867138
143 rdf:type schema:CreativeWork
144 https://doi.org/10.4171/cmh/110 schema:sameAs https://app.dimensions.ai/details/publication/pub.1072316207
145 rdf:type schema:CreativeWork
146 https://doi.org/10.4310/maa.2011.v18.n2.a1 schema:sameAs https://app.dimensions.ai/details/publication/pub.1072461465
147 rdf:type schema:CreativeWork
148 https://www.grid.ac/institutes/grid.10388.32 schema:alternateName University of Bonn
149 schema:name Universität Bonn, Bonn, Germany
150 rdf:type schema:Organization
151 https://www.grid.ac/institutes/grid.5970.b schema:alternateName International School for Advanced Studies
152 schema:name SISSA, Trieste, Italy
153 University of Nice, Nice, France
154 rdf:type schema:Organization
155 https://www.grid.ac/institutes/grid.9681.6 schema:alternateName University of Jyväskylä
156 schema:name University of Jyväskylä, Jyväskylä, Finland
157 rdf:type schema:Organization
 




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


...