The paper "How many cages midscribe an egg?” authored by Prof.LIU Jinsong and his student Ph.D ZHOU Ze, from AMSS was accepted for publication on Invent. Math. The Midscribability Theorem, which was first proved by O. Schramm, states that: given a strictly convex body K⊂R 3 with smooth boundary and a convex polyhedron P, there exists a polyhedron Q⊂RP 3 combinatorially equivalent to P which midscribes K. Here the word "midscribe" means that all its edges are tangent to the boundary surface of K. By using of the intersection number technique, together with the Teichm\"{u}ller theory of packings, the paper provides an alternative approach to this theorem. Furthermore, combining Schramm's method with the above ones, the authors prove a rigidity result concerning this theorem as well. Namely, such a polyhedron is unique under certain normalization conditions. . Prof.LIU got his Ph.D degree from Peking University in 2002. His research interests cover Teichmuller & Moduli Space, Quadratic Differentials, Computational Conformal Geometry and Circle Packing. |
