Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Curvature estimates for the level sets of solutions of the
  Monge-Amp\`{e}re equation $\det D^2 u=1$   For the Monge-Amp\`{e}re equation $\det D^2 u=1$, we find new auxiliary
curvature functions which attain respective maximum on the boundary. Moreover,
we obtain the upper bounded estimates for the Gauss curvature and mean
curvature of the level sets for the solution to this equation.

21
The categories of this paper are: adap-org
1
The categories of this paper are: cs
32
The categories of this paper are: atom-ph
18
The categories of this paper are: econ
7
The categories of this paper are: hep-th
4
The categories of this paper are: cond-mat
15
The categories of this paper are: nucl-ex
10
The categories of this paper are: q-bio
22
The categories of this paper are: chao-dyn
24
The categories of this paper are: dg-ga
23
The categories of this paper are: solv-int
6
The categories of this paper are: astro-ph
11
The categories of this paper are: hep-lat
9
The categories of this paper are: nlin
28
The categories of this paper are: alg-geom
31
The categories of this paper are: ao-sci