Jinsong Liu, Chinese Academy of Sciences, Beijing

Deformation of circle patterns and its applications

Abstract

Given a circle pattern on the Riemann sphere , in this talk we prove that its quasiconformal deformation space can be naturally identified with the product of the Teichmüller spaces of its interstices.

By using the intersection number technique, together with Teichmüller theory of packings, we provides an alternative approach to the Midscribability Theorem. Furthermore, by combining Schramm's method with the above ones, we obtain a rigidity result as well. Furthermore, by using these methods, we shall investigate the stability of some inscribable graphs.