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Topology/Geometry Seminar

Ideal Hyperbolic Polyhedra and Discrete Uniformization 

Boris Springborn (Berlin)

Location:  Hill 705
Date & time: Tuesday, 17 September 2019 at 3:50PM - 4:40PM

Abstract:   Two seemingly unrelated problems turn out to be equivalent. The first is a problem of 3-dimensional hyperbolic geometry: Given a complete hyperbolic surface of finite area that is homeomorphic to a sphere with punctures, find a realization as convex ideal polyhedron in hyperbolic space. The second is a problem of discrete complex analysis: Given a closed triangle mesh of genus zero, find a discretely conformally equivalent convex triangle mesh inscribed in a sphere. The existence and uniqueness of a solution of the first (hence also the second) problem was shown by I. Rivin. His proof is not constructive. A variational principle leads to a new constructive proof.