Cut and singular loci up to codimension 3

[Cut-loci et lieux singuliers jusqu’à codimension 3]

Ardoy, Pablo Angulo ; Guijarro, Luis

Annales de l'Institut Fourier, Tome 61 (2011), p. 1655-1681 / Harvested from Numdam

Résumé

Le cut locus d’une variété Finslerienne peut être non-triangulable, mais une description locale à tous les points sauf pour un ensemble de dimension de Hausdorff $n-2$ est bien connu. Nous donnons une nouvelle description de la structure de ces ensembles, avec des applications directes pour les ensembles des points singuliers de certaines équations de Hamilton-Jacobi. Nous donnons une classification de tous les points sauf pour un ensemble de dimension de Hausdorff $n-3$.

Abstract

We give a new and detailed description of the structure of cut loci, with direct applications to the singular sets of some Hamilton-Jacobi equations. These sets may be non-triangulable, but a local description at all points except for a set of Hausdorff dimension $n-2$ is well known. We go further in this direction by giving a classification of all points up to a set of Hausdorff dimension $n-3$.

Détail

Publié le : 2011-01-01

MR 2951748 | Zbl 1242.35095

DOI : https://doi.org/10.5802/aif.2655
Classification:  35F30,  53C60,  53B40
Mots clés: cut locus, équations de Hamilton-Jacobi, points focaux

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