Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Unclouding the sky of negatively curved manifolds   Let M be a complete simply connected Riemannian manifold, with sectional
curvature K bounded above by -1. Under some assumptions on the geometry of the
boundary of M, which are satisfied for instance if M is a symmetric space, or
has dimension 2, we prove that given any family of horoballs in M, and any
point x_0 outside these horoballs, it is possible to shrink uniformly, by a
finite amount depending only on M, these horoballs so that some geodesic ray
starting from x_0 avoids the shrunk horoballs. As an application, we give a
uniform upper bound on the infimum of the heights of the closed geodesics in
the finite volume quotients of M.

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The categories of this paper are: plasm-ph
36
The categories of this paper are: cmp-lg
17
The categories of this paper are: q-fin
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The categories of this paper are: supr-con
3
The categories of this paper are: physics
13
The categories of this paper are: quant-ph
8
The categories of this paper are: hep-ex
4
The categories of this paper are: cond-mat
25
The categories of this paper are: patt-sol
16
The categories of this paper are: stat
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The categories of this paper are: atom-ph
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The categories of this paper are: dg-ga
11
The categories of this paper are: hep-lat
22
The categories of this paper are: chao-dyn
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The categories of this paper are: funct-an
28
The categories of this paper are: alg-geom