Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Escobar's Conjecture on a sharp lower bound for the first nonzero
  Steklov eigenvalue   It was conjectured by Escobar [J. Funct. Anal. 165 (1999), 101-116] that for
an $n$-dimensional ($n\geq 3$) smooth compact Riemannian manifold with
boundary, which has nonnegative Ricci curvature and boundary principal
curvatures bounded below by $c>0$, the first nonzero Steklov eigenvalue is
greater than or equal to $c$ with equality holding only on isometrically
Euclidean balls with radius $1/c$. In this paper, we confirm this conjecture in
the case of nonnegative sectional curvature. The proof is based on a
combination of Qiu-Xia's weighted Reilly type formula with a special choice of
the weight function depending on the distance function to the boundary, as well
as a generalized Pohozaev type identity.

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The categories of this paper are: comp-gas
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The categories of this paper are: funct-an
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The categories of this paper are: cond-mat
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The categories of this paper are: math-ph
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The categories of this paper are: chem-ph
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The categories of this paper are: hep-lat
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The categories of this paper are: cmp-lg
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The categories of this paper are: q-bio
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The categories of this paper are: adap-org
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The categories of this paper are: supr-con
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The categories of this paper are: astro-ph
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The categories of this paper are: cs
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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: plasm-ph
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The categories of this paper are: solv-int