摘要
设f:D→D'是一个拟共形映射,D,D'为R^(n)上的区域.设e,e'分别为D,D'中的内相似度量,D关于e是一个φ-broad区域.作者首先证明了,若A■D使得f(A)关于'是线性局部连通、有界转向的,则f|A:A→f(A)在度量e,e'下是弱拟对称的.其次,作者证明了对D中任意弧连通子集A,若f|A:A→f(A)关于度量e,'为弱拟对称映射,则f|A为拟对称映射.
Let f:D→D′be a quasiconformal mapping,where D and D′are domains in R^(n).Let e and e′be two internally-like metrics of D and D′respectively,and D be-broad with respect to e.The authors first show that if A■D is such that f(A)is linearly locally connected set and bounded turning with respect to e′in D′,then f|A:A→f(A)is weakly quasisymmetric in the metrics e and e′.Secondly,the authors prove that for every arcwise connected subset A in D,if f|A:A→f(A)is weakly quasisymmetric in the metrics e and e′,then it is quasisymmetric.
作者
黄体仁
张秋莹
HUANG Tiren;ZHANG Qiuying(Science of School,Zhejiang Sci-Tech University,Hangzhou 310018,China;Jinhua Open University,Jinhua 321000,Zhejiang,China)
出处
《数学年刊(A辑)》
北大核心
2025年第1期75-100,共26页
Chinese Annals of Mathematics
基金
国家自然科学基金(No.11271118)的资助。
关键词
拟共形映射
拟对称映射
度量空间
Quasiconformal mapping
Quasisymmetric mapping
Metric space
