Combinatorial Ricci and Calabi flows on discrete conformal structures over surfaces with boundary are proven to converge exponentially to prescribed boundary lengths, globally for two structure classes and locally for the others.
Combinatorial Yamabe flow on hyperbolic bordered surfaces
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abstract
This paper studies the combinatorial Yamabe flow on hyperbolic bordered surfaces. We show that the flow exists for all time and converges exponentially fast to conformal factor which produces a hyperbolic surface whose lengths of boundary components are equal to prescribed positive numbers. This provides an algorithm to such problems.
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Discrete conformal structures on surfaces with boundary (III) -- Deformation
Combinatorial Ricci and Calabi flows on discrete conformal structures over surfaces with boundary are proven to converge exponentially to prescribed boundary lengths, globally for two structure classes and locally for the others.