Singular gradient flow of the distance function and homotopy equivalence View Full Text


Ontology type: schema:ScholarlyArticle     


Article Info

DATE

2013-05

AUTHORS

P. Albano, P. Cannarsa, Khai T. Nguyen, C. Sinestrari

ABSTRACT

Let be a Riemannian manifold and let be a bounded open subset of . It is well known that significant information about the geometry of is encoded into the properties of the distance, , from the boundary of . Here, we show that the generalized gradient flow associated with the distance preserves singularities, that is, if is a singular point of then the generalized characteristic starting at stays singular for all times. As an application, we deduce that the singular set of has the same homotopy type as . More... »

PAGES

23-43

References to SciGraph publications

  • 1992-12. On the singularities of convex functions in MANUSCRIPTA MATHEMATICA
  • 2002-03. Propagation of Singularities¶for Solutions of Nonlinear First Order¶Partial Differential Equations in ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS
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  • 1992. Riemannian Geometry in NONE
  • 2003. A Panoramic View of Riemannian Geometry in NONE
  • 2009. Optimal Transport, Old and New in NONE
  • Identifiers

    URI

    http://scigraph.springernature.com/pub.10.1007/s00208-012-0835-8

    DOI

    http://dx.doi.org/10.1007/s00208-012-0835-8

    DIMENSIONS

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