Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Fractal Weyl laws for asymptotically hyperbolic manifolds   For asymptotically hyperbolic manifolds with hyperbolic trapped sets we prove
a fractal upper bound on the number of resonances near the essential spectrum,
with power determined by the dimension of the trapped set. This covers the case
of general convex cocompact quotients (including the case of connected trapped
sets) where our result implies a bound on the number of zeros of the Selberg
zeta function in disks of arbitrary size along the imaginary axis. Although no
sharp fractal lower bounds are known, the case of quasifuchsian groups,
included here, is most likely to provide them.

36
The categories of this paper are: cmp-lg
16
The categories of this paper are: stat
31
The categories of this paper are: ao-sci
19
The categories of this paper are: eess
9
The categories of this paper are: nlin
23
The categories of this paper are: solv-int
30
The categories of this paper are: q-alg
15
The categories of this paper are: nucl-ex
22
The categories of this paper are: chao-dyn
1
The categories of this paper are: cs
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The categories of this paper are: funct-an
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The categories of this paper are: adap-org
24
The categories of this paper are: dg-ga
8
The categories of this paper are: hep-ex
27
The categories of this paper are: comp-gas
28
The categories of this paper are: alg-geom