Generalized gradient flow and singularities of the Riemannian distance function | Zendy

Piermarco Cannarsa | Zendy

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Generalized gradient flow and singularities of the Riemannian distance function

Author(s) -

Piermarco Cannarsa

Publication year - 2014

Publication title -

séminaire laurent schwartz — edp et applications

Language(s) - English

Resource type - Journals

ISSN - 2266-0607

DOI - 10.5802/slsedp.37

Subject(s) - mathematics , homotopy , bounded function , equivalence (formal languages) , boundary (topology) , gravitational singularity , riemannian manifold , manifold (fluid mechanics) , geometric flow , pure mathematics , function (biology) , domain (mathematical analysis) , mathematical analysis , topology (electrical circuits) , balanced flow , flow (mathematics) , geometry , combinatorics , mechanical engineering , evolutionary biology , engineering , biology

Significant information about the topology of a bounded domain Ω of a Riemannian manifold M is encoded into the properties of the distance, d∂Ω, from the boundary of Ω. We discuss recent results showing the invariance of the singular set of the distance function with respect to the generalized gradient flow of d∂Ω, as well as applications to homotopy equivalence.

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