Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Hyperbolic polyhedra and discrete uniformization   We provide a constructive, variational proof of Rivin's realization theorem
for ideal hyperbolic polyhedra with prescribed intrinsic metric, which is
equivalent to a discrete uniformization theorem for spheres. The same
variational method is also used to prove a discrete uniformization theorem of
Gu et al. and a corresponding polyhedral realization result of Fillastre. The
variational principles involve twice continuously differentiable functions on
the decorated Teichm\"uller spaces $\widetilde{\mathcal{T}_{g,n}}$ of punctured
surfaces, which are analytic in each Penner cell, convex on each fiber over
$\mathcal{T}_{g,n}$, and invariant under the action of the mapping class group.

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The categories of this paper are: chem-ph
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The categories of this paper are: atom-ph
1
The categories of this paper are: cs
4
The categories of this paper are: cond-mat
16
The categories of this paper are: stat
22
The categories of this paper are: chao-dyn
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The categories of this paper are: comp-gas
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The categories of this paper are: mtrl-th
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The categories of this paper are: ao-sci
5
The categories of this paper are: gr-qc
8
The categories of this paper are: hep-ex
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The categories of this paper are: nucl-th
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The categories of this paper are: patt-sol
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The categories of this paper are: hep-th
33
The categories of this paper are: plasm-ph
28
The categories of this paper are: alg-geom