Is there always an extremal Teichmüller mapping?

被引：3
作者：
Guowu Yao
机构：
[1] Chinese Academy of Sciences,Institute of Mathematics Academy of Mathematics and Systems Science
来源：
Journal d’Analyse Mathematique | 2004年 / 94卷
关键词：
Riemann Surface; Quasiconformal Mapping; Extremal Mapping; Jordan Domain; Maximal Dilatation;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
Given a quasisymmetric self-homeomorphismh of the unit circleS1, letQ(h) be the set of all quasiconformal mappings with the boundary correspondenceh. In [1], it was shown that there existsh for which no extremal extension inQ(h) as a Teichmüller mapping is possible. This disproved some conjectures of long standing. In the example constructed there, the boundary correspondence has a single extremal quasiconformal extension. We show that even when there are infinitely many extremal extensions of the boundary values, it may still happen that none of the extensions is a Teichmüller mapping. An infinitesimal version of this result is also obtained.
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页码：363 / 375
页数：12
相关论文
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