Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Effective results on uniformization and intrinsic GCM spheres in
  perturbations of Kerr   This is a follow-up of our paper \cite{KS-Kerr1} on the construction of
general covariant modulated (GCM) spheres in perturbations of Kerr, which we
expect to play a central role in establishing their nonlinear stability. We
reformulate the main results of that paper using a canonical definition of
$\ell=1$ modes on a $2$-sphere embedded in a $1+3$ vacuum manifold. This is
based on a new, effective, version of the classical uniformization theorem
which allows us to define such modes and prove their stability for spheres with
comparable metrics. The reformulation allows us to prove a second, intrinsic,
existence theorem for GCM spheres, expressed purely in terms of geometric
quantities defined on it. A natural definition of angular momentum for such GCM
spheres is also introduced, which we expect to play a key role in determining
the final angular momentum for general perturbations of Kerr.

25
The categories of this paper are: patt-sol
33
The categories of this paper are: plasm-ph
10
The categories of this paper are: q-bio
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The categories of this paper are: cmp-lg
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The categories of this paper are: eess
11
The categories of this paper are: hep-lat
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The categories of this paper are: ao-sci
32
The categories of this paper are: atom-ph
18
The categories of this paper are: econ
29
The categories of this paper are: funct-an
4
The categories of this paper are: cond-mat
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The categories of this paper are: solv-int
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The categories of this paper are: quant-ph
9
The categories of this paper are: nlin
12
The categories of this paper are: nucl-th
35
The categories of this paper are: mtrl-th