Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Flag area measures   A flag area measure on an $n$-dimensional euclidean vector space is a
continuous translation-invariant valuation with values in the space of signed
measures on the flag manifold consisting of a unit vector $v$ and a
$(p+1)$-dimensional linear subspace containing $v$ with $0 \leq p \leq n-1$.
  Using local parallel sets, Hinderer constructed examples of
$\mathrm{SO}(n)$-covariant flag area measures. There is an explicit formula for
his flag area measures evaluated on polytopes, which involves the squared
cosine of the angle between two subspaces.
  We construct a more general sequence of smooth $\mathrm{SO}(n)$-covariant
flag area measures via integration over the normal cycle of appropriate
differential forms. We provide an explicit description of our measures on
polytopes, which involves an arbitrary elementary symmetric polynomial in the
squared cosines of the principal angles between two subspaces.
  Moreover, we show that these flag area measures span the space of all smooth
$\mathrm{SO}(n)$-covariant flag area measures, which gives a classification
result in the spirit of Hadwiger's theorem.

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The categories of this paper are: hep-th
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The categories of this paper are: alg-geom
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The categories of this paper are: nucl-ex
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The categories of this paper are: q-fin
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The categories of this paper are: econ
29
The categories of this paper are: funct-an
1
The categories of this paper are: cs
27
The categories of this paper are: comp-gas
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The categories of this paper are: hep-lat
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The categories of this paper are: solv-int
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The categories of this paper are: hep-ex
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The categories of this paper are: astro-ph
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The categories of this paper are: gr-qc
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The categories of this paper are: plasm-ph
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The categories of this paper are: cond-mat
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The categories of this paper are: supr-con