Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Strong Sard Conjecture and regularity of singular minimizing geodesics
  for analytic sub-Riemannian structures in dimension 3   In this paper we prove the strong Sard conjecture for sub-Riemannian
structures on 3-dimensional analytic manifolds. More precisely, given a totally
nonholonomic analytic distribution of rank 2 on a 3-dimensional analytic
manifold, we investigate the size of the set of points that can be reached by
singular horizontal paths starting from a given point and prove that it has
Hausdorff dimension at most 1. In fact, provided that the lengths of the
singular curves under consideration are bounded with respect to a given
complete Riemannian metric, we demonstrate that such a set is a semianalytic
curve. As a consequence, combining our techniques with recent developments on
the regularity of sub-Riemannian minimizing geodesics, we prove that minimizing
sub-Riemannian geodesics in 3-dimensional analytic manifolds are always of
class C 1 , and actually are analytic outside of a finite set of points.

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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: chao-dyn
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The categories of this paper are: adap-org
31
The categories of this paper are: ao-sci
17
The categories of this paper are: q-fin
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The categories of this paper are: q-bio
18
The categories of this paper are: econ
13
The categories of this paper are: quant-ph
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The categories of this paper are: dg-ga
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The categories of this paper are: cmp-lg
33
The categories of this paper are: plasm-ph
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The categories of this paper are: stat
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The categories of this paper are: math-ph
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The categories of this paper are: funct-an
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The categories of this paper are: nucl-ex