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Modulus of surface families and the radial stretch in the Heisenberg group

Published online by Cambridge University Press:  26 May 2016

IOANNIS D. PLATIS
IOANNIS D. PLATIS*
Affiliation:
Department of Mathematics and Applied Mathematics, University of Crete, GR 70013 Heraklion Crete, Greece. e-mail: jplatis@math.uoc.gr
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Abstract

We develop a modulus method for surface families inside a domain in the Heisenberg group and we prove that the stretch map between two Heisenberg spherical rings is a minimiser for the mean distortion among the class of contact quasiconformal maps between these rings which satisfy certain boundary conditions.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 162 , Issue 1 , January 2017 , pp. 13 - 37
Copyright
Copyright © Cambridge Philosophical Society 2016 

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