Cut and singular loci up to codimension 3

Pablo Angulo Ardoy[1]; Luis Guijarro[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

Annales de l’institut Fourier (2011)

  • Volume: 61, Issue: 4, page 1655-1681
  • ISSN: 0373-0956

Abstract

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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 .

How to cite

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Ardoy, Pablo Angulo, and Guijarro, Luis. "Cut and singular loci up to codimension 3." Annales de l’institut Fourier 61.4 (2011): 1655-1681. <http://eudml.org/doc/219811>.

@article{Ardoy2011,
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 $n-3$.},
affiliation = {Universidad Autónoma de Madrid Departamento de Matemáticas Facultad de Ciencias Campus de Cantoblanco 28049 Madrid (Spain); Department of Mathematics Universidad Autónoma de Madrid. Please complete ICMAT CSIC-UAM-UCM-UC3M},
author = {Ardoy, Pablo Angulo, Guijarro, Luis},
journal = {Annales de l’institut Fourier},
keywords = {Cut locus; Hamilton-Jacobi equations; focal points; cut locus},
language = {eng},
number = {4},
pages = {1655-1681},
publisher = {Association des Annales de l’institut Fourier},
title = {Cut and singular loci up to codimension 3},
url = {http://eudml.org/doc/219811},
volume = {61},
year = {2011},
}

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
PB - Association des Annales de l’institut Fourier
VL - 61
IS - 4
SP - 1655
EP - 1681
AB - 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 $n-3$.
LA - eng
KW - Cut locus; Hamilton-Jacobi equations; focal points; cut locus
UR - http://eudml.org/doc/219811
ER -

References

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