Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Ancient solutions for flow by powers of the curvature in $\mathbb R^2$   We construct a new compact convex embedded ancient solution of the
$\kappa^\alpha$ flow in $\mathbb R^2$, $\alpha\in(\frac12,1)$ that lies between
two parallel lines. Using this solution we classify all convex ancient
solutions of the $\kappa^\alpha$ flow in $\mathbb R^2$, for
$\alpha\in(\frac23,1)$. Moreover, we show that any non-compact convex embedded
ancient solution of the $\kappa^\alpha$ flow in $\mathbb R^2$,
$\alpha\in(\frac12,1)$ must be a translating solution.

25
The categories of this paper are: patt-sol
28
The categories of this paper are: alg-geom
26
The categories of this paper are: bayes-an
7
The categories of this paper are: hep-th
27
The categories of this paper are: comp-gas
29
The categories of this paper are: funct-an
35
The categories of this paper are: mtrl-th
16
The categories of this paper are: stat
6
The categories of this paper are: astro-ph
1
The categories of this paper are: cs
24
The categories of this paper are: dg-ga
34
The categories of this paper are: chem-ph
15
The categories of this paper are: nucl-ex
30
The categories of this paper are: q-alg
36
The categories of this paper are: cmp-lg
9
The categories of this paper are: nlin