no. 4
Cut and singular loci up to codimension 3
[Cut-loci et lieux singuliers jusqu’à codimension 3]
Ardoy, Pablo Angulo1 ; Guijarro, Luis2
1 Universidad Autónoma de Madrid Departamento de Matemáticas Facultad de Ciencias Campus de Cantoblanco 28049 Madrid (Spain)
2 Department of Mathematics Universidad Autónoma de Madrid. Please complete ICMAT CSIC-UAM-UCM-UC3M
Annales de l'Institut Fourier, Tome 61 (2011) no. 4, pp. 1655-1681.

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.

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.

DOI : 10.5802/aif.2655
Classification : 35F30, 53C60, 53B40
Keywords: Cut locus, Hamilton-Jacobi equations, focal points
Mot clés : cut locus, équations de Hamilton-Jacobi, points focaux

Ardoy, Pablo Angulo 1 ; Guijarro, Luis 2

1 Universidad Autónoma de Madrid Departamento de Matemáticas Facultad de Ciencias Campus de Cantoblanco 28049 Madrid (Spain)
2 Department of Mathematics Universidad Autónoma de Madrid. Please complete ICMAT CSIC-UAM-UCM-UC3M 
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Ardoy, Pablo Angulo; Guijarro, Luis. Cut and singular loci up to codimension 3. Annales de l'Institut Fourier, Tome 61 (2011) no. 4, pp. 1655-1681. doi : 10.5802/aif.2655. https://aif.centre-mersenne.org/articles/10.5802/aif.2655/

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