Cut and singular loci up to codimension 3

Details Cut and singular loci up to codimension 3 Cut and singular loci up to codimension 3

2008-06-13

arxiv.org/abs/0806.2229v2

Mathematics

Analysis of PDEs

19 pages, 1 figure

Scientific paper

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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