Seminar November 22 – Kei Nakamura

On November 22nd, Kei Nakamura will speak in the the Geometry-Topology Seminar. He will speak about:

Title: On convex and non-convex Fuchsian polyhedral realizations of hyperbolic surfaces with a single conical singularity

Abstract: For a hyperbolic surface S with genus g \geq 2 and with some conical singularities of positive curvatures, its Fuchsian polyhedral realization is an incompressible isometric embedding of S in a Fuchsian cylinder H^3/\Gamma for some Fuchsian group \Gamma with genus g such that the image is a piecewise totally geodesic polyhedral surface. It is known by a theorem of Fillastre that, for any such S, there exists a unique convex Fuchsian polyhedral realization. We will describe the geometry of convex and non-convex Fuchsian polyhedral realizations when S has a single conical singularity, and show that the convex case indeed corresponds to the Delaunay triangulation of S. Joint work with Jaejeong Lee.

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