Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The shape of hyperbolic Dehn surgery space   In this paper we develop a new theory of infinitesimal harmonic deformations
for compact hyperbolic 3-manifolds with ``tubular boundary''. In particular,
this applies to complements of tubes of radius at least $R_0 =
\arctanh(1/\sqrt{3}) \approx 0.65848$ around the singular set of hyperbolic
cone manifolds, removing the previous restrictions on cone angles.
  We then apply this to obtain a new quantitative version of Thurston's
hyperbolic Dehn surgery theorem, showing that all generalized Dehn surgery
coefficients outside a disc of ``uniform'' size yield hyperbolic structures.
Here the size of a surgery coefficient is measured using the Euclidean metric
on a horospherical cross section to a cusp in the complete hyperbolic metric,
rescaled to have area 1. We also obtain good estimates on the change in
geometry (e.g. volumes and core geodesic lengths) during hyperbolic Dehn
filling.
  This new harmonic deformation theory has also been used by Bromberg and his
coworkers in their proofs of the Bers Density Conjecture for Kleinian groups.

25
The categories of this paper are: patt-sol
20
The categories of this paper are: acc-phys
28
The categories of this paper are: alg-geom
37
The categories of this paper are: supr-con
16
The categories of this paper are: stat
10
The categories of this paper are: q-bio
11
The categories of this paper are: hep-lat
7
The categories of this paper are: hep-th
13
The categories of this paper are: quant-ph
5
The categories of this paper are: gr-qc
29
The categories of this paper are: funct-an
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The categories of this paper are: solv-int
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The categories of this paper are: chao-dyn
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The categories of this paper are: ao-sci
30
The categories of this paper are: q-alg
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The categories of this paper are: plasm-ph