Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Kinematic formulae for tensorial curvature measures   Tensorial curvature measures are tensor-valued generalizations of the
curvature measures of convex bodies. We prove a complete set of kinematic
formulae for such tensorial curvature measures on convex bodies and for their
(nonsmooth) generalizations on convex polytopes. These formulae express the
integral mean of the tensorial curvature measure of the intersection of two
given convex bodies (resp.~polytopes), one of which is uniformly moved by a
proper rigid motion, in terms of linear combinations of tensorial curvature
measures of the given convex bodies (resp.~polytopes). We prove these results
in a more direct way than in the classical proof of the principal kinematic
formula for curvature measures, which uses the connection to Crofton formulae
to determine the involved constants explicitly.

31
The categories of this paper are: ao-sci
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The categories of this paper are: hep-ph
30
The categories of this paper are: q-alg
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The categories of this paper are: q-fin
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The categories of this paper are: quant-ph
6
The categories of this paper are: astro-ph
4
The categories of this paper are: cond-mat
20
The categories of this paper are: acc-phys
12
The categories of this paper are: nucl-th
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The categories of this paper are: econ
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The categories of this paper are: cmp-lg
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The categories of this paper are: solv-int
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The categories of this paper are: nlin
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The categories of this paper are: dg-ga
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The categories of this paper are: chem-ph
11
The categories of this paper are: hep-lat