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Generalized gradient flow and singularities of the Riemannian distance function

Piermarco Cannarsa (2012/2013)

Séminaire Laurent Schwartz — EDP et applications

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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