Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Isoperimetric inequality under Measure-Contraction property   We prove that if $(X,\mathsf d,\mathfrak m)$ is an essentially non-branching
metric measure space with $\mathfrak m(X)=1$, having Ricci curvature bounded
from below by $K$ and dimension bounded from above by $N \in (1,\infty)$,
understood as a synthetic condition called Measure-Contraction property, then a
sharp isoperimetric inequality \`a la L\'evy-Gromov holds true. Measure
theoretic rigidity is also obtained.

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The categories of this paper are: nucl-th
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The categories of this paper are: ao-sci
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The categories of this paper are: chem-ph
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The categories of this paper are: funct-an
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The categories of this paper are: alg-geom
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The categories of this paper are: hep-ph
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The categories of this paper are: acc-phys
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The categories of this paper are: adap-org
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The categories of this paper are: cmp-lg
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The categories of this paper are: q-bio
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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: mtrl-th
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The categories of this paper are: econ
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The categories of this paper are: astro-ph
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The categories of this paper are: patt-sol