Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The Extension for Mean Curvature Flow with Finite Integral Curvature in
  Riemannian Manifolds   We investigate the integral conditions to extend the mean curvature flow in a
Riemannian manifold. We prove that the mean curvature flow solution with finite
total mean curvature on a finite time interval $[0,T)$ can be extended over
time $T$. Moreover, we show that the condition is optimal in some sense.

28
The categories of this paper are: alg-geom
3
The categories of this paper are: physics
23
The categories of this paper are: solv-int
18
The categories of this paper are: econ
6
The categories of this paper are: astro-ph
24
The categories of this paper are: dg-ga
21
The categories of this paper are: adap-org
5
The categories of this paper are: gr-qc
35
The categories of this paper are: mtrl-th
37
The categories of this paper are: supr-con
1
The categories of this paper are: cs
19
The categories of this paper are: eess
33
The categories of this paper are: plasm-ph
26
The categories of this paper are: bayes-an
22
The categories of this paper are: chao-dyn
27
The categories of this paper are: comp-gas