Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Non-collapsing in mean-convex mean curvature flow   We provide a direct proof of a non-collapsing estimate for compact
hypersurfaces with positive mean curvature moving under the mean curvature
flow: Precisely, if every point on the initial hypersurface admits an interior
sphere with radius inversely proportional to the mean curvature at that point,
then this remains true for all positive times in the interval of existence.

32
The categories of this paper are: atom-ph
18
The categories of this paper are: econ
8
The categories of this paper are: hep-ex
24
The categories of this paper are: dg-ga
19
The categories of this paper are: eess
6
The categories of this paper are: astro-ph
4
The categories of this paper are: cond-mat
28
The categories of this paper are: alg-geom
36
The categories of this paper are: cmp-lg
29
The categories of this paper are: funct-an
31
The categories of this paper are: ao-sci
9
The categories of this paper are: nlin
26
The categories of this paper are: bayes-an
10
The categories of this paper are: q-bio
13
The categories of this paper are: quant-ph
22
The categories of this paper are: chao-dyn