Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Convex ancient solutions of the mean curvature flow   We study solutions of the mean curvature flow which are defined for all
negative curvature times, usually called ancient solutions. We give various
conditions ensuring that a closed convex ancient solution is a shrinking
sphere. Examples of such conditions are: a uniform pinching condition on the
curvatures, a suitable growth bound on the diameter or a reverse isoperimetric
inequality. We also study the behaviour of uniformly k-convex solutions, and
consider generalizations to ancient solutions immersed in a sphere.

18
The categories of this paper are: econ
7
The categories of this paper are: hep-th
34
The categories of this paper are: chem-ph
22
The categories of this paper are: chao-dyn
33
The categories of this paper are: plasm-ph
36
The categories of this paper are: cmp-lg
27
The categories of this paper are: comp-gas
30
The categories of this paper are: q-alg
19
The categories of this paper are: eess
1
The categories of this paper are: cs
26
The categories of this paper are: bayes-an
14
The categories of this paper are: math-ph
16
The categories of this paper are: stat
17
The categories of this paper are: q-fin
11
The categories of this paper are: hep-lat
9
The categories of this paper are: nlin