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math.GT2026
Discrete uniformization of polyhedral surfaces
Feng Luo, Yanwen Luo, Zhenghao Rao +1
The main result of the paper shows that each connected polyhedral surface with a hyperbolic background metric, or a Euclidean background metric with uniformly bounded circumdisk ra…
math.GT2026
Morphing Graphs on Hyperbolic Surfaces
Yanwen Luo, Yuan Luo
We propose the first algorithm to morph geometric graphs on hyperbolic surfaces. It is based on a generalization of Tutte's spring embedding theorem on essentially 3-vertex-connect…
math.GT2026
A Rigidity Theorem for Convex Sets in Hyperbolic 3-Space
Feng Luo, Yanwen Luo, Zhenghao Rao
Pogorelov's rigidity theorem states that a compact convex body in the hyperbolic 3-space is determined up to isometry by the intrinsic path metric on its boundary. The main result…