Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the Inner Radius of Nodal Domains   Let M be a closed Riemannian manifold. We consider the inner radius of a
nodal domain for a large eigenvalue \lambda. We give upper and lower bounds on
the inner radius of the type C/\lambda^k. Our proof is based on a local
behavior of eigenfunctions discovered by Donnelly and Fefferman, and a
Poincar\'e type inequality proved by Maz'ya. Sharp lower bounds are known only
in dimension two. We give an account of this case too.

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The categories of this paper are: nucl-th
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The categories of this paper are: hep-ph
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The categories of this paper are: quant-ph
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The categories of this paper are: acc-phys
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The categories of this paper are: comp-gas
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The categories of this paper are: stat
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The categories of this paper are: q-bio
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The categories of this paper are: supr-con
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The categories of this paper are: bayes-an
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The categories of this paper are: physics
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The categories of this paper are: eess
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The categories of this paper are: cmp-lg
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The categories of this paper are: funct-an
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The categories of this paper are: nlin
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The categories of this paper are: math-ph
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The categories of this paper are: chem-ph