Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Size of the medial axis and stability of Federer's curvature measures   In this article, we study the (d-1)-volume and the covering numbers of the
medial axis of a compact set of the Euclidean d-space. In general, this volume
is infinite; however, the (d-1)-volume and covering numbers of a filtered
medial axis (the mu-medial axis) that is at distance greater than R from the
compact set will be explicitely bounded. The behaviour of the bound we obtain
with respect to mu, R and the covering numbers of the compact set K are
optimal.
  From this result we deduce that the projection function on a compact subset K
of the Euclidean d-space depends continuously on the compact set K, in the L^1
sense. This implies in particular that Federer's curvature measure of a compact
set with positive reach can be reliably estimated from a Hausdorff
approximation of this set, regardless of any regularity assumption on the
approximation.

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The categories of this paper are: physics
28
The categories of this paper are: alg-geom
18
The categories of this paper are: econ
29
The categories of this paper are: funct-an
6
The categories of this paper are: astro-ph
10
The categories of this paper are: q-bio
15
The categories of this paper are: nucl-ex
37
The categories of this paper are: supr-con
22
The categories of this paper are: chao-dyn
33
The categories of this paper are: plasm-ph
32
The categories of this paper are: atom-ph
16
The categories of this paper are: stat
36
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: gr-qc
34
The categories of this paper are: chem-ph