Cut and singular loci up to codimension 3

2008/06/13 by Pablo Angulo Ardoy, Luis Guijarro, Ardoy, Pablo Angulo +1
Mathematics · Physics and Astronomy · #35F30 #53B40 #53C60 #Algebraic structures and combinatorial models #Analysis of PDEs (math.AP) #Differential Geometry (math.DG) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Nonlinear Waves and Solitons

paper · pdf · doi:10.48550/arxiv.0806.2229

openalex publication_date 2008/06/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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 clasification of all points up to a set of Hausdorff dimension n-3.

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