Generalized gradient flow and singularities of the Riemannian distance function

Piermarco Cannarsa[1]

  • [1] Dipartimento di Matematica Università di Roma ‘Tor Vergata’ Via della Ricerca Scientifica 1 00133 Roma Italy

Séminaire Laurent Schwartz — EDP et applications (2012-2013)

  • Volume: 2012-2013, page 1-16
  • ISSN: 2266-0607

Abstract

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

How to cite

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Cannarsa, Piermarco. "Generalized gradient flow and singularities of the Riemannian distance function." Séminaire Laurent Schwartz — EDP et applications 2012-2013 (2012-2013): 1-16. <http://eudml.org/doc/275792>.

@article{Cannarsa2012-2013,
abstract = {Significant information about the topology of a bounded domain $\Omega $ of a Riemannian manifold $M$ is encoded into the properties of the distance, $d_\{\partial \Omega \}$, from the boundary of $\Omega $. We discuss recent results showing the invariance of the singular set of the distance function with respect to the generalized gradient flow of $d_\{\partial \Omega \}$, as well as applications to homotopy equivalence.},
affiliation = {Dipartimento di Matematica Università di Roma ‘Tor Vergata’ Via della Ricerca Scientifica 1 00133 Roma Italy},
author = {Cannarsa, Piermarco},
journal = {Séminaire Laurent Schwartz — EDP et applications},
keywords = {generalized characteristics; semiconcavity; generalized gradient flow},
language = {eng},
pages = {1-16},
publisher = {Institut des hautes études scientifiques & Centre de mathématiques Laurent Schwartz, École polytechnique},
title = {Generalized gradient flow and singularities of the Riemannian distance function},
url = {http://eudml.org/doc/275792},
volume = {2012-2013},
year = {2012-2013},
}

TY - JOUR
AU - Cannarsa, Piermarco
TI - Generalized gradient flow and singularities of the Riemannian distance function
JO - Séminaire Laurent Schwartz — EDP et applications
PY - 2012-2013
PB - Institut des hautes études scientifiques & Centre de mathématiques Laurent Schwartz, École polytechnique
VL - 2012-2013
SP - 1
EP - 16
AB - Significant information about the topology of a bounded domain $\Omega $ of a Riemannian manifold $M$ is encoded into the properties of the distance, $d_{\partial \Omega }$, from the boundary of $\Omega $. We discuss recent results showing the invariance of the singular set of the distance function with respect to the generalized gradient flow of $d_{\partial \Omega }$, as well as applications to homotopy equivalence.
LA - eng
KW - generalized characteristics; semiconcavity; generalized gradient flow
UR - http://eudml.org/doc/275792
ER -

References

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