Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A Convergence Result for the Gradient Flow of $\int |A|^2$ in Riemannian
  Manifolds   We study the gradient flow of the $L^2-$norm of the second fundamental form
of smooth immersions of two-dimensional surfaces into compact Riemannian
manifolds. By analogy with the results obtained for the Willmore flow in
Riemannian manifolds, we prove lifespan estimates in terms of the
$L^2-$concentration of the second fundamental form of the initial data and we
show existence of blowup limits. Under special condition both on the initial
data and on the target manifold, we prove a long time existence result for the
flow and subconvergence to a critical immersion.

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The categories of this paper are: cs
31
The categories of this paper are: ao-sci
30
The categories of this paper are: q-alg
35
The categories of this paper are: mtrl-th
29
The categories of this paper are: funct-an
12
The categories of this paper are: nucl-th
10
The categories of this paper are: q-bio
20
The categories of this paper are: acc-phys
33
The categories of this paper are: plasm-ph
16
The categories of this paper are: stat
0
The categories of this paper are: hep-ph
6
The categories of this paper are: astro-ph
26
The categories of this paper are: bayes-an
9
The categories of this paper are: nlin
11
The categories of this paper are: hep-lat
14
The categories of this paper are: math-ph