Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A note on propagation of singularities of semiconcave functions of two
  variables   P. Albano and P. Cannarsa proved in 1999 that, under some applicable
conditions, singularities of semiconcave functions in $\R^n$ propagate along
Lipschitz arcs. Further regularity properties of these arcs were proved by P.
Cannarsa and Y. Yu in 2009. We prove that, for $n=2$, these arcs are very
regular: they can be found in the form (in a suitable Cartesian coordinate
system) $\psi(x) = (x, y_1(x)-y_2(x)), x \in [0,\alpha]$, where $y_1$, $y_2$
are convex and Lipschitz on $[0,\alpha]$. In other words: singularities
propagate along arcs with finite turn.

22
The categories of this paper are: chao-dyn
36
The categories of this paper are: cmp-lg
34
The categories of this paper are: chem-ph
4
The categories of this paper are: cond-mat
35
The categories of this paper are: mtrl-th
21
The categories of this paper are: adap-org
33
The categories of this paper are: plasm-ph
12
The categories of this paper are: nucl-th
25
The categories of this paper are: patt-sol
32
The categories of this paper are: atom-ph
11
The categories of this paper are: hep-lat
19
The categories of this paper are: eess
13
The categories of this paper are: quant-ph
7
The categories of this paper are: hep-th
31
The categories of this paper are: ao-sci
0
The categories of this paper are: hep-ph