Rigidity of Circle Packings and Sphere Packings

  • [2017-06-13]

    Spearker:XU Xu, Wuhan University


    Room:Room 1518,School of Mathematical Sciences

    Detail: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.

    Organizer: School of Mathematical Sciences


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