Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: New Developments in Mean Curvature Flow of Arbitrary Codimension
  Inspired By Yau Rigidity Theory   In this survey, we will focus on the mean curvature flow theory with sphere
theorems, and discuss the recent developments on the convergence theorems for
the mean curvature flow of arbitrary codimension inspired by the Yau rigidity
theory of submanifolds. Several new differentiable sphere theorems for
submanifolds are obtained as consequences of the convergence theorems for the
mean curvature flow. It should be emphasized that Theorem 4.1 is an optimal
convergence theorem for the mean curvature flow of arbitrary codimension, which
implies the first optimal differentiable sphere theorem for submanifolds with
positive Ricci curvature. Finally, we present a list of unsolved problems in
this area.

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The categories of this paper are: supr-con
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The categories of this paper are: chao-dyn
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The categories of this paper are: stat
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The categories of this paper are: quant-ph
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The categories of this paper are: adap-org
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The categories of this paper are: ao-sci
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The categories of this paper are: nucl-th
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The categories of this paper are: nlin
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The categories of this paper are: math-ph
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The categories of this paper are: acc-phys
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The categories of this paper are: dg-ga
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The categories of this paper are: hep-ph
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The categories of this paper are: astro-ph
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The categories of this paper are: cmp-lg
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The categories of this paper are: cs
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The categories of this paper are: chem-ph