Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Combinatorial Calabi flows on surfaces   For triangulated surfaces, we introduce the combinatorial Calabi flow which
is an analogue of smooth Calabi flow. We prove that the solution of
combinatorial Calabi flow exists for all time. Moreover, the solution converges
if and only if Thurston's circle packing exists. As a consequence,
combinatorial Calabi flow provides a new algorithm to find circle packings with
prescribed curvatures. The proofs rely on careful analysis of combinatorial
Calabi energy, combinatorial Ricci potential and discrete dual-Laplacians.

30
The categories of this paper are: q-alg
18
The categories of this paper are: econ
28
The categories of this paper are: alg-geom
15
The categories of this paper are: nucl-ex
29
The categories of this paper are: funct-an
23
The categories of this paper are: solv-int
4
The categories of this paper are: cond-mat
36
The categories of this paper are: cmp-lg
8
The categories of this paper are: hep-ex
9
The categories of this paper are: nlin
26
The categories of this paper are: bayes-an
3
The categories of this paper are: physics
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The categories of this paper are: plasm-ph
24
The categories of this paper are: dg-ga
37
The categories of this paper are: supr-con
0
The categories of this paper are: hep-ph