Name Jiming Ma Fudan University Session Jan 11 14:50~15:20 E11-102 Delaunay 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. 102-1-11/8eak-ma.pdf