Name  Jiming Ma 

Affiliation  Fudan University 
Talk type  Session 
Time  Jan 11 14:50~15:20 
Location  E11102 
Title  Delaunay inversive distance circle packings and hyperideal Fuchsian polyhedra with particles 
Abstract 
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 3dimensional hyperbolic geometry and variational principle. This is a joint work with JeanMarc Schlenker.

Slide  102111/8eakma.pdf 