NameJiming Ma
AffiliationFudan University
Talk typeSession
TimeJan 11 14:50~15:20
TitleDelaunay inversive distance circle packings and hyperideal Fuchsian polyhedra with particles
Fixed $\Theta=(\theta_1, \theta_2, \cdots, \theta_{n})\in (0, \pi)^{n}$, let $\mathscr{T}_{g,n}$ be the Teichm\"uller space of marked hyperbolic surfaces of genus $g$ with $n$ infinite area ends, we prove: 1. Delaunay inversive distance circle packings on $\Theta$ conical hyperbolic surfaces are parameterized by $\mathscr{T}_{g,n}$. We also prove the rigidity of Delaunay inversive distance circle packings. 2. The space $\mathscr{P}_{g,n}$ of hyperideal Fuchsian polyhedra with particles admits the given angles $\Theta$ is homeomorphic to $\mathscr{T}_{g,n}$. These two results are proved simultaneously through 3-dimensional hyperbolic geometry and variational principle. This is a joint work with Jean-Marc Schlenker.