Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Curvature estimates for the level set of spatial quasiconcave solutions
  to a class of parabolic equations   We prove a constant rank theorem for the second fundamental form of the
spatial convex level surfaces of solutions to equations $u_t=F(\n^2u, \n u, u,
t)$ under a structural condition, and give a geometric lower bound of the
principal curvature of the spatial level surfaces.

0
The categories of this paper are: hep-ph
29
The categories of this paper are: funct-an
18
The categories of this paper are: econ
32
The categories of this paper are: atom-ph
7
The categories of this paper are: hep-th
36
The categories of this paper are: cmp-lg
31
The categories of this paper are: ao-sci
6
The categories of this paper are: astro-ph
10
The categories of this paper are: q-bio
13
The categories of this paper are: quant-ph
1
The categories of this paper are: cs
17
The categories of this paper are: q-fin
11
The categories of this paper are: hep-lat
14
The categories of this paper are: math-ph
21
The categories of this paper are: adap-org
23
The categories of this paper are: solv-int