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Rigidity of quasiconformal maps on Carnot groups

Published online by Cambridge University Press:  06 June 2016

XIANGDONG XIE
XIANGDONG XIE*
Affiliation:
Dept. of Mathematics and Statistics, Bowling Green State University, Bowling Green, OH, U.S.A. e-mail: xiex@bgsu.edu
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Abstract

We show that quasiconformal maps on many Carnot groups must be biLipschitz. In particular, this is the case for 2-step Carnot groups with reducible first layer. These results have implications for the rigidity of quasiisometries between negatively curved solvable Lie groups.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 162 , Issue 1 , January 2017 , pp. 131 - 150
Copyright
Copyright © Cambridge Philosophical Society 2016 

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