高维空间中的有界凸域

Bounded and Convex Domains in ■~n

证明n维空间中的有界凸域D能被拟共形映射到n维单位球B^n(0,1),即D是拟球,从而说明拟共形映射中的黎曼定理在n维空间中的有界凸域类中是成立的．

We prove that every bounded and convex domain in R^n can be mapped onto B^n（0,1） by a quasiconformal mapping of R^n,i.e.,it is a quasiball.This shows that the Riemann mapping theorem of n-dimensioanl quasiconformal mappings holds in the class of bounded and convex domains in R^n.