Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Rigidity for nearly umbilical hypersurfaces in space forms   Perez proved some $L^2$ inequalities for closed convex hypersurfaces immersed
in the Euclidean space $\mathbb{R}^{n+1}$, more generally, for closed
hypersurfaces with non-negative Ricci curvature, immersed in an Einstein
manifold. In this paper, we discuss the rigidity of these inequalities when the
ambient manifold is $\mathbb{R}^{n+1}$, the hyperbolic space
$\mathbb{H}^{n+1}$, or the closed hemisphere $\mathbb{S}_+^{n+1}$. We also
obtain a generalization of the Perez's theorem to the hypersurfaces without the
hypothesis of non-negative Ricci curvature.

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The categories of this paper are: chem-ph
28
The categories of this paper are: alg-geom
18
The categories of this paper are: econ
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The categories of this paper are: comp-gas
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The categories of this paper are: acc-phys
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The categories of this paper are: eess
33
The categories of this paper are: plasm-ph
0
The categories of this paper are: hep-ph
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The categories of this paper are: nucl-ex
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The categories of this paper are: cmp-lg
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The categories of this paper are: math-ph
5
The categories of this paper are: gr-qc
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The categories of this paper are: hep-th
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The categories of this paper are: nlin
4
The categories of this paper are: cond-mat
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The categories of this paper are: dg-ga