Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On hypersurfaces of positive reach, alternating Steiner formulae and
  Hadwiger's Problem   We give new characterisations of sets of positive reach and show that a
closed hypersurface has positive reach if and only if it is of class $C^{1,1}$.
These results are then used to prove new alternating Steiner formul{\ae} for
hypersurfaces of positive reach. Furthermore, it will turn out that every
hypersurface that satisfies an alternating Steiner formula has positive reach.
Finally, we provide a new solution to a problem by Hadwiger on convex sets and
prove long time existence for the gradient flow of mean breadth.

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The categories of this paper are: cs
20
The categories of this paper are: acc-phys
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The categories of this paper are: quant-ph
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The categories of this paper are: math-ph
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The categories of this paper are: econ
10
The categories of this paper are: q-bio
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The categories of this paper are: eess
8
The categories of this paper are: hep-ex
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The categories of this paper are: patt-sol
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The categories of this paper are: q-fin
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The categories of this paper are: chem-ph
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The categories of this paper are: cmp-lg
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The categories of this paper are: dg-ga
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The categories of this paper are: hep-lat
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The categories of this paper are: stat
30
The categories of this paper are: q-alg