Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the regularity of Cauchy hypersurfaces and temporal functions in
  closed cone structures   We complement our work on the causality of upper semi-continuous
distributions of cones with some results on Cauchy hypersurfaces. We prove that
every locally stably acausal Cauchy hypersurface is stable. Then we prove that
the signed distance $d_S$ from a spacelike hypersurface $S$ is, in a
neighborhood of it, as regular as the hypersurface, and by using this fact we
give a proof that every Cauchy hypersurface is the level set of a Cauchy
temporal (and steep) function of the same regularity as the hypersurface. We
also show that in a globally hyperbolic closed cone structure compact spacelike
hypersurfaces with boundary can be extended to Cauchy spacelike hypersurfaces
of the same regularity. We end the work with a separation result and a density
result.

34
The categories of this paper are: chem-ph
13
The categories of this paper are: quant-ph
7
The categories of this paper are: hep-th
10
The categories of this paper are: q-bio
35
The categories of this paper are: mtrl-th
27
The categories of this paper are: comp-gas
37
The categories of this paper are: supr-con
4
The categories of this paper are: cond-mat
22
The categories of this paper are: chao-dyn
31
The categories of this paper are: ao-sci
1
The categories of this paper are: cs
18
The categories of this paper are: econ
11
The categories of this paper are: hep-lat
23
The categories of this paper are: solv-int
32
The categories of this paper are: atom-ph
3
The categories of this paper are: physics