Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: First stability eigenvalue of singular minimal hypersurfaces in spheres   In this short note we extend an estimate due to J. Simons on the first
stability eigenvalue of minimal hypersurfaces in spheres to the singular
setting. Specifically, we show that any singular minimal hypersurface in
$S^{n+1}$, which is not totally geodesic and satisfies the \alpha-structural
hypothesis, has first stability eigenvalue at most -2n, with equality if and
only if it is a product of two round spheres. The equality case was settled
independently in the classical setting by Wu and Perdomo.

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The categories of this paper are: hep-ex
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The categories of this paper are: q-alg
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The categories of this paper are: hep-lat
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The categories of this paper are: adap-org
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The categories of this paper are: econ
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The categories of this paper are: quant-ph
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The categories of this paper are: astro-ph
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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: stat
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The categories of this paper are: physics
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The categories of this paper are: solv-int
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The categories of this paper are: alg-geom
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The categories of this paper are: q-fin
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The categories of this paper are: atom-ph
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The categories of this paper are: math-ph