Convex hull theorem for multiply connected domains in the plane with an estimate of the quasiconformal constant  

作　　者：LIU Gang WU ShengJian 

机构地区：[1]LMAM,School of Mathematical Sciences,Peking University,Beijing 100871,China

出　　处：《Science China Mathematics》2009年第5期932-940,共9页中国科学：数学（英文版）

基　　金：supported by National Natural Science Foundation of China (Grant Nos. 10671004, 10831004);the Doctoral Education Program Foundation of China (Grant No. 20060001003)

摘　　要：For any multiply connected domain Ω in ?2, let S be the boundary of the convex hull in H 3 of ?2Ω which faces Ω. Suppose in addition that there exists a lower bound l > 0 of the hyperbolic lengths of closed geodesics in Ω. Then there is always a K-quasiconformal mapping from S to Ω, which extends continuously to the identity on ?S = ?Ω, where K depends only on l. We also give a numerical estimate of K by using the parameter l.For any multiply connected domain Ω in R2, let S be the boundary of the convex hull in H3 of R2\Ω which faces Ω. Suppose in addition that there exists a lower bound l > 0 of the hyperbolic lengths of closed geodesics in Ω. Then there is always a K-quasiconformal mapping from S to Ω, which extends continuously to the identity on S = Ω, where K depends only on l. We also give a numerical estimate of K by using the parameter l.

关 键 词：convex hull quasiconformal mapping multiply connected domain 30C62 

分 类 号：O211.67[理学—概率论与数理统计]