Combinatorial Yamabe flow on hyperbolic surfaces with boundary

Details Combinatorial Yamabe flow on hyperbolic surfaces with boundary Combinatorial Yamabe flow on hyperbolic surfaces with boundary

2010-03-20

arxiv.org/abs/1003.3910v1

Communications in Contemporary Mathematics Vol. 13, No. 5 (2011) 827--842

Mathematics

Geometric Topology

10 pages

Scientific paper

This paper studies the combinatorial Yamabe flow on hyperbolic surfaces with
boundary. It is proved by applying a variational principle that the length of
boundary components is uniquely determined by the combinatorial conformal
factor. The combinatorial Yamabe flow is a gradient flow of a concave function.
The long time behavior of the flow and the geometric meaning is investigated.

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