Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Harmonic deformations of hyperbolic 3-manifolds   This paper gives an exposition of the authors' harmonic deformation theory
for 3-dimensional hyperbolic cone-manifolds. We discuss topological
applications to hyperbolic Dehn surgery as well as recent applications to
Kleinian group theory. A central idea is that local rigidity results (for
deformations fixing cone angles) can be turned into effective control on the
deformations that do exist. This leads to precise analytic and geometric
versions of the idea that hyperbolic structures with short geodesics are close
to hyperbolic structures with cusps. The paper also outlines a new harmonic
deformation theory which applies whenever there is a sufficiently large
embedded tube around the singular locus, removing the previous restriction to
cone angles at most 2pi.

9
The categories of this paper are: nlin
18
The categories of this paper are: econ
29
The categories of this paper are: funct-an
37
The categories of this paper are: supr-con
36
The categories of this paper are: cmp-lg
15
The categories of this paper are: nucl-ex
4
The categories of this paper are: cond-mat
23
The categories of this paper are: solv-int
16
The categories of this paper are: stat
25
The categories of this paper are: patt-sol
10
The categories of this paper are: q-bio
33
The categories of this paper are: plasm-ph
21
The categories of this paper are: adap-org
11
The categories of this paper are: hep-lat
32
The categories of this paper are: atom-ph
20
The categories of this paper are: acc-phys