Title：Rigidity of circle packings and sphere packings

Spearker：徐旭（武汉大学）

Time：2017年6月13日（周二）   下午15:00-16:00

Room：东区管理科研楼  数学科学学院1518室

Abstract：In this talk, we will first give an introduction to Andreev-Thurston Theorem for circle packings on surfaces with non-obtuse intersection angles, which implies the existence and uniqueness of hyperbolic metrics on 3-dimensional polyhedrons. Then we will extend the Andreev-Thurston Theorem to the case including obtuse intersection angles. Inversive distance circle packing metric is a generalization of Thurston's circle packing metric. Bowers and Stephensononce conjectured that the inversive distance circle packings are globally rigid. Ren Guo and Feng Luo proved that the conjecture is true for nonnegative inversive distances. In this talk, we will present a proof of Bowers and Stephenson's conjecture for the case including negative inversive distances. We also extend the circle packings on surfaces to sphere packings on 3-manifolds and prove the global rigidity conjectured by Cooper and Rivin, which implies the uniqueness of hyperbolic metrics on 4-dimensional polyhedrons.