Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A quantitative version of a theorem by Jungreis   A fundamental result by Gromov and Thurston asserts that, if M is a closed
hyperbolic n-manifold, then the simplicial volume |M| of M is equal to
vol(M)/v_n, where v_n is a constant depending only on the dimension of M. The
same result also holds for complete finite-volume hyperbolic manifolds without
boundary, while Jungreis proved that the ratio vol(M)/|M| is strictly smaller
than v_n if M is compact with non-empty geodesic boundary. We prove here a
quantitative version of Jungreis' result for n>3, which bounds from below the
ratio |M|/vol(M) in terms of the ratio between the volume of the boundary of M
and the volume of M. As a consequence, we show that a sequence {M_i} of compact
hyperbolic n-manifolds with geodesic boundary is such that the limit of
vol(M_i)/|M_i| equals v_n if and only if the volume of the boundary of M_i
grows sublinearly with respect to the volume of the boundary of M_i. We also
provide estimates of the simplicial volume of hyperbolic manifolds with
geodesic boundary in dimension three.

4
The categories of this paper are: cond-mat
5
The categories of this paper are: gr-qc
20
The categories of this paper are: acc-phys
35
The categories of this paper are: mtrl-th
28
The categories of this paper are: alg-geom
33
The categories of this paper are: plasm-ph
0
The categories of this paper are: hep-ph
27
The categories of this paper are: comp-gas
29
The categories of this paper are: funct-an
11
The categories of this paper are: hep-lat
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The categories of this paper are: q-bio
18
The categories of this paper are: econ
31
The categories of this paper are: ao-sci
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The categories of this paper are: atom-ph
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The categories of this paper are: hep-th
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The categories of this paper are: nucl-ex