Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Stochastic Properties of the Laplacian on Riemannian Submersions   Based on ideas of Pigolla and Setti \cite{PS} we prove that immersed
submanifolds with bounded mean curvature of Cartan-Hadamard manifolds are
Feller. We also consider Riemannian submersions $\pi \colon M \to N$ with
compact minimal fibers, and based on various criteria for parabolicity and
stochastic completeness, see \cite{Grygor'yan}, we prove that $M$ is Feller,
parabolic or stochastically complete if and only if the base $N$ is Feller,
parabolic or stochastically complete respectively.

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The categories of this paper are: eess
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The categories of this paper are: astro-ph
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The categories of this paper are: dg-ga
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The categories of this paper are: solv-int
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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: nucl-ex
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The categories of this paper are: acc-phys
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The categories of this paper are: nucl-th
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The categories of this paper are: gr-qc
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The categories of this paper are: q-alg
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The categories of this paper are: alg-geom
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The categories of this paper are: physics
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The categories of this paper are: adap-org
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The categories of this paper are: bayes-an
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The categories of this paper are: atom-ph