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Combinatorial Yamabe flow on hyperbolic surfaces with boundary

Published 20 Mar 2010 in math.GT and math.DG | (1003.3910v1)

Abstract: 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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