Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Estimates of the first Dirichlet eigenvalue from exit time moment
  spectra   We compute the first Dirichlet eigenvalue of a geodesic ball in a
rotationally symmetric model space in terms of the moment spectrum for the
Brownian motion exit times from the ball. This expression implies an estimate
as exact as you want for the first Dirichlet eigenvalue of a geodesic ball in
these rotationally symmetric spaces, including the real space forms of constant
curvature. As an application of the model space theory we prove lower and upper
bounds for the first Dirichlet eigenvalues of extrinsic metric balls in
submanifolds of ambient Riemannian spaces which have model space controlled
curvatures. Moreover, from this general setting we thereby obtain new
generalizations of the classical and celebrated results due to McKean and
Cheung--Leung concerning the fundamental tones of Cartan-Hadamard manifolds and
the fundamental tones of submanifolds with bounded mean curvature in hyperbolic
spaces, respectively.

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The categories of this paper are: physics
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The categories of this paper are: nucl-ex
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The categories of this paper are: gr-qc
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The categories of this paper are: mtrl-th
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The categories of this paper are: q-bio
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The categories of this paper are: q-alg
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The categories of this paper are: chem-ph
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The categories of this paper are: alg-geom
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The categories of this paper are: dg-ga
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The categories of this paper are: acc-phys
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The categories of this paper are: eess
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The categories of this paper are: nlin
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The categories of this paper are: patt-sol
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The categories of this paper are: q-fin
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The categories of this paper are: hep-lat
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The categories of this paper are: solv-int