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 is well known. We go further in this direction by giving a classification of all points up to a set of Hausdorff dimension .
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 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 .
Keywords: Cut locus, Hamilton-Jacobi equations, focal points
Mot clés : cut locus, équations de Hamilton-Jacobi, points focaux
@article{AIF_2011__61_4_1655_0, author = {Ardoy, Pablo Angulo and Guijarro, Luis}, title = {Cut and singular loci up to codimension 3}, journal = {Annales de l'Institut Fourier}, pages = {1655--1681}, publisher = {Association des Annales de l{\textquoteright}institut Fourier}, volume = {61}, number = {4}, year = {2011}, doi = {10.5802/aif.2655}, zbl = {1242.35095}, mrnumber = {2951748}, language = {en}, url = {http://www.numdam.org/articles/10.5802/aif.2655/} }
TY - JOUR AU - Ardoy, Pablo Angulo AU - Guijarro, Luis TI - Cut and singular loci up to codimension 3 JO - Annales de l'Institut Fourier PY - 2011 SP - 1655 EP - 1681 VL - 61 IS - 4 PB - Association des Annales de l’institut Fourier UR - http://www.numdam.org/articles/10.5802/aif.2655/ DO - 10.5802/aif.2655 LA - en ID - AIF_2011__61_4_1655_0 ER -
%0 Journal Article %A Ardoy, Pablo Angulo %A Guijarro, Luis %T Cut and singular loci up to codimension 3 %J Annales de l'Institut Fourier %D 2011 %P 1655-1681 %V 61 %N 4 %I Association des Annales de l’institut Fourier %U http://www.numdam.org/articles/10.5802/aif.2655/ %R 10.5802/aif.2655 %G en %F AIF_2011__61_4_1655_0
Ardoy, Pablo Angulo; Guijarro, Luis. Cut and singular loci up to codimension 3. Annales de l'Institut Fourier, Volume 61 (2011) no. 4, pp. 1655-1681. doi : 10.5802/aif.2655. http://www.numdam.org/articles/10.5802/aif.2655/
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