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