| 黄体仁,张秋莹.R^n中内相似度量下的拟共形映射和拟对称映射[J].数学年刊A辑,2025,46(1):75~100 |
| R^n中内相似度量下的拟共形映射和拟对称映射 |
| Quasiconformal and Quasisymmetric Mappings in Rn with Internally-like Metrics |
| Received:September 01, 2023 Revised:February 07, 2025 |
| DOI：10.16205/j.cnki.cama.2025.0004 |
| 中文关键词: 拟共形映射 拟对称映射 度量空间 |
| 英文关键词:Quasiconformal mapping Quasisymmetric mapping Metric space |
| 基金项目:本文受到国家自然科学基金(No.11271118) |
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| 中文摘要: |
| 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?-broad区域. 作者首先证明了, 若A∈D使得f(A)关于e'是线性局部连通、有界转向的, 则f|A: A→(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, e'为弱拟对称映射, 则f|A为拟对称映射. |
| 英文摘要: |
| Let f : D → D′ be a quasiconformal mapping, where D and D′ are domains in
Rn. 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. |
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