Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Cut and singular loci up to codimension 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 clasification of all points up to a set of Hausdorff
dimension $n-3$.

16
The categories of this paper are: stat
29
The categories of this paper are: funct-an
32
The categories of this paper are: atom-ph
31
The categories of this paper are: ao-sci
20
The categories of this paper are: acc-phys
0
The categories of this paper are: hep-ph
35
The categories of this paper are: mtrl-th
26
The categories of this paper are: bayes-an
6
The categories of this paper are: astro-ph
3
The categories of this paper are: physics
13
The categories of this paper are: quant-ph
37
The categories of this paper are: supr-con
15
The categories of this paper are: nucl-ex
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The categories of this paper are: dg-ga
5
The categories of this paper are: gr-qc
17
The categories of this paper are: q-fin