Let M be a Riemannian manifold and let Omega be a bounded open subset of M. It is well known that significant information about the geometry of Omega is encoded into the properties of the distance, d , from the boundary of Omega. Here, we show that the generalized gradient flow associated with the distance preserves singularities, that is, if x_0 is a singular point of d then the generalized characteristic starting at x_0 stays singular for all times. As an application, we deduce that the singular set of d has the same homotopy type as Omega.

Albano, P., Cannarsa, P., Nguyen, K., Sinestrari, C. (2013). Singular gradient flow of the distance function and homotopy equivalence. MATHEMATISCHE ANNALEN, 356(1), 23-43 [10.1007/s00208-012-0835-8].

Singular gradient flow of the distance function and homotopy equivalence

CANNARSA, PIERMARCO;SINESTRARI, CARLO
2013-01-01

Abstract

Let M be a Riemannian manifold and let Omega be a bounded open subset of M. It is well known that significant information about the geometry of Omega is encoded into the properties of the distance, d , from the boundary of Omega. Here, we show that the generalized gradient flow associated with the distance preserves singularities, that is, if x_0 is a singular point of d then the generalized characteristic starting at x_0 stays singular for all times. As an application, we deduce that the singular set of d has the same homotopy type as Omega.
2013
Pubblicato
Rilevanza internazionale
Articolo
Esperti anonimi
Settore MAT/05 - ANALISI MATEMATICA
English
Con Impact Factor ISI
Albano, P., Cannarsa, P., Nguyen, K., Sinestrari, C. (2013). Singular gradient flow of the distance function and homotopy equivalence. MATHEMATISCHE ANNALEN, 356(1), 23-43 [10.1007/s00208-012-0835-8].
Albano, P; Cannarsa, P; Nguyen, K; Sinestrari, C
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2108/89937
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