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. |