Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A semigroup approach to Finsler geometry: Bakry-Ledoux's isoperimetric
  inequality   We develop the celebrated semigroup approach \`a la Bakry et al on Finsler
manifolds, where natural Laplacian and heat semigroup are nonlinear, based on
the Bochner-Weitzenb\"ock formula established by Sturm and the author. We show
the $L^1$-gradient estimate on Finsler manifolds (under some additional
assumptions in the noncompact case), which is equivalent to a lower weighted
Ricci curvature bound and the improved Bochner inequality. As a geometric
application, we prove Bakry-Ledoux's Gaussian isoperimetric inequality, again
under some additional assumptions in the noncompact case. This extends
Cavalletti-Mondino's inequality on reversible Finsler manifolds to
non-reversible metrics, and improves the author's previous estimate, both based
on the localization (also called needle decomposition) method.

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The categories of this paper are: acc-phys
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The categories of this paper are: bayes-an
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The categories of this paper are: nucl-ex
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The categories of this paper are: nlin
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The categories of this paper are: hep-ex
25
The categories of this paper are: patt-sol
3
The categories of this paper are: physics
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The categories of this paper are: astro-ph
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The categories of this paper are: q-fin
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The categories of this paper are: adap-org
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The categories of this paper are: cond-mat
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The categories of this paper are: funct-an
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The categories of this paper are: econ
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The categories of this paper are: atom-ph
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The categories of this paper are: quant-ph
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The categories of this paper are: cmp-lg