Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Talenti's comparison theorem for Poisson equation and applications on
  Riemannian manifold with nonnegative Ricci curvature   In this article, we prove Talenti's comparison theorem for Poisson equation
on complete noncompact Riemannian manifold with nonnegative Ricci curvature.
Furthermore, we obtain the Faber-Krahn inequality for the first eigenvalue of
Dirichlet Laplacian, $L^1$- and $L^\infty$-moment spectrum, especially
Saint-Venant theorem for torsional rigidity and a reverse H\"older inequality
for eigenfunctions of Dirichlet Laplacian.

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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: stat
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The categories of this paper are: nlin
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The categories of this paper are: acc-phys
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The categories of this paper are: q-alg
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The categories of this paper are: funct-an
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The categories of this paper are: supr-con
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The categories of this paper are: q-bio
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The categories of this paper are: solv-int
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The categories of this paper are: nucl-ex
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The categories of this paper are: atom-ph
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The categories of this paper are: eess
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The categories of this paper are: hep-th
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The categories of this paper are: quant-ph
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The categories of this paper are: hep-ex