Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Hopf type Theorem for Self-Shrinkers   In this paper, we prove that a two-dimensional self-shrinker, homeomorphic to
the sphere, immersed in the three dimensional Euclidean space is a round
sphere, provided its mean curvature and the norm of its position vector have an
upper bound in terms of the norm of its traceless second fundamental form. The
example constructed by Drugan justifies that the hypothesis on the second
fundamental form is necessary. We can also prove the same kind of rigidity
results for surfaces with parallel weighted mean curvature vector in R n with
radial weight. These results are applications of a new generalization of
Cauchy's Theorem in complex analysis which concludes that a complex function is
identically zero or its zeroes are isolated if it satisfies some weak
holomorphy.

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The categories of this paper are: eess
26
The categories of this paper are: bayes-an
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The categories of this paper are: atom-ph
6
The categories of this paper are: astro-ph
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The categories of this paper are: patt-sol
4
The categories of this paper are: cond-mat
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The categories of this paper are: econ
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The categories of this paper are: cmp-lg
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The categories of this paper are: ao-sci
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The categories of this paper are: alg-geom
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The categories of this paper are: chem-ph
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The categories of this paper are: gr-qc
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The categories of this paper are: stat
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The categories of this paper are: nucl-ex
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The categories of this paper are: dg-ga
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The categories of this paper are: quant-ph