Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Adiabatic Isometric Mapping Algorithm for Embedding 2-Surfaces in
  Euclidean 3-Space   Alexandrov proved that any simplicial complex homeomorphic to a sphere with
strictly non-negative Gaussian curvature at each vertex can be isometrically
embedded uniquely in $\mathbb{R}^3$ as a convex polyhedron. Due to the
nonconstructive nature of his proof, there have yet to be any algorithms, that
we know of, that realizes the Alexandrov embedding in polynomial time.
Following his proof, we developed the adiabatic isometric mapping (AIM)
algorithm. AIM uses a guided adiabatic pull-back procedure to produce "smooth"
embeddings. Tests of AIM applied to two different polyhedral metrics suggests
that its run time is sub cubic with respect to the number of vertices. Although
Alexandrov's theorem specifically addresses the embedding of convex polyhedral
metrics, we tested AIM on a broader class of polyhedral metrics that included
regions of negative Gaussian curvature. One test was on a surface just outside
the ergosphere of a Kerr black hole.

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The categories of this paper are: eess
35
The categories of this paper are: mtrl-th
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The categories of this paper are: plasm-ph
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The categories of this paper are: cs
3
The categories of this paper are: physics
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The categories of this paper are: funct-an
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The categories of this paper are: acc-phys
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The categories of this paper are: q-bio
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The categories of this paper are: bayes-an
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The categories of this paper are: cmp-lg
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The categories of this paper are: nlin
4
The categories of this paper are: cond-mat
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The categories of this paper are: q-alg
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The categories of this paper are: quant-ph
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The categories of this paper are: ao-sci
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The categories of this paper are: dg-ga