Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On an extension of the H^{k} mean curvature flow   In this note we generalize an extension theorem in [5] and [9] of the mean
curvature flow to the H^{k} mean curvature flow under some extra conditions.
The main difficult problem in proving the extension theorem is to find a
suitable version of Michael-Simon inequality for the H^{k} mean curvature flow,
and to do a suitable Moser iteration process. These two problems are overcame
by imposing some extra conditions which may be weakened or removed in our
forthcoming paper [7]. On the other hand, we derive some estimates for the
generalized mean curvature flow, which have their own interesting.

17
The categories of this paper are: q-fin
37
The categories of this paper are: supr-con
4
The categories of this paper are: cond-mat
33
The categories of this paper are: plasm-ph
30
The categories of this paper are: q-alg
31
The categories of this paper are: ao-sci
10
The categories of this paper are: q-bio
1
The categories of this paper are: cs
0
The categories of this paper are: hep-ph
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The categories of this paper are: math-ph
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The categories of this paper are: stat
8
The categories of this paper are: hep-ex
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The categories of this paper are: comp-gas
5
The categories of this paper are: gr-qc
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The categories of this paper are: chao-dyn
12
The categories of this paper are: nucl-th