圆堆积及其拟共形形变研究

Now circle packing has been studied rather extensively by many mathematicians. This program is to study circle packing and its quasiconformal deformation theory. It includes the following parts: 1. We will give a further estimate of the rigidity constants of the hexagonal circle packing. And we will give the expansion of the rigidity constant. In particular we will study the geometric properties of the 2-generation circle packings in the complex plane. 2：When the domain is bounded and smooth, we will give a global estimatate of the error between the circle packing mappings and the Riemann mapping. 3. We will study the inscribable problem. That is, given a smooth strictly convex body K and a convex polyhedron P in R^3, is there a some convex polyhedron Q combinatorically equivalent to P which inscibes K

现在圆堆积（Circle Packing）理论受到了大家广泛的关注。本项目主要研究Circle Packing以及它的拟共形形变理论。主要包含以下几个方面的内容： 1: 研究平面上的六边形的Circle Packing 的刚性常数的精细估计，并试图给出它的完全展 开式；我们还将研究2 重极值circle packing 的几何性质。 2：当区域是有界光滑时，研究圆堆积离散映射和黎曼映照之间的整体误差。 3: 给定凸体K，在给定骨架下，研究K的内接凸多面体的存在性。

现在圆堆积（Circle Packing）理论受到了大家广泛的关注。本项目主要研究Circle Packing以及它的拟共形形变理论以及相关问题。主要包含以下几个方面的内容：1: Circle packing形变理论及其应用；2：给定凸体K，在给定骨架下，研究K的内接凸多面体的存在性； 3：把动力系统中整数群作用系统子集合的Bowen熵推广了顺从群作用系统子集合的Bowen熵。