Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Robin Heat Semigroup and HWI Inequality on Manifolds with Boundary   Let $M$ be a complete connected Riemannian manifold with boundary $\pp M$,
$Q$ a bounded continuous function on $\pp M$, and $L= \DD+Z$ for a $C^1$-vector
field $Z$ on $M$. By using the reflecting diffusion process generated by $L$
and its local time on the boundary, a probabilistic formula is presented for
the semigroup generated by $L$ on $M$ with Robin boundary condition $N,\nn
f+Qf=0,$ where $N$ is the inward unit normal vector field of $\pp M$. As an
application, the HWI inequality is established on manifolds with (nonconvex)
boundary. In order to study this semigroup, Hsu's gradient estimate and the
corresponding Bismut's derivative formula are established on a class of
noncompact manifolds with boundary.

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The categories of this paper are: nucl-th
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The categories of this paper are: stat
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The categories of this paper are: atom-ph
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The categories of this paper are: bayes-an
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The categories of this paper are: eess
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The categories of this paper are: adap-org
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The categories of this paper are: gr-qc
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The categories of this paper are: cmp-lg
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The categories of this paper are: cs
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The categories of this paper are: supr-con
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The categories of this paper are: nucl-ex
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The categories of this paper are: econ
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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: quant-ph
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The categories of this paper are: comp-gas