Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Michael-Simon inequalities for $k$-th mean curvatures   This paper continues the study of Alexandrov-Fenchel inequalities for
quermassintegrals for $k$-convex domains. It focuses on the application to the
Michael-Simon type inequalities for $k$-curvature operators. The proof uses
optimal transport maps as a tool to relate curvature quantities defined on the
boundary of a domain.

4
The categories of this paper are: cond-mat
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The categories of this paper are: q-bio
11
The categories of this paper are: hep-lat
26
The categories of this paper are: bayes-an
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The categories of this paper are: eess
35
The categories of this paper are: mtrl-th
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The categories of this paper are: hep-ex
37
The categories of this paper are: supr-con
31
The categories of this paper are: ao-sci
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The categories of this paper are: cs
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The categories of this paper are: gr-qc
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The categories of this paper are: patt-sol
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The categories of this paper are: solv-int
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The categories of this paper are: econ
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The categories of this paper are: acc-phys
36
The categories of this paper are: cmp-lg