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Extremal Length Decomposition and Domain Constants for Finitely Connected Domains

Extremal Length Decomposition and Domain Constants for Finitely Connected Domains This paper is concerned with the study of quasi-extremal distance domains, a class of domains introduced by Gehring and Martio in connection with the theory of quasiconformal mappings. We obtain a sharp upper bound for the quasi-extremal distance constant $$M(\Omega )$$ M ( Ω ) of a finitely connected planar domain in terms of local boundary dilatation of its boundary components. For the proof of the main theorem, several independently interesting results are also established. One of them is a decomposition lemma about the extremal length of a curve family. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Computational Methods and Function Theory Springer Journals

Extremal Length Decomposition and Domain Constants for Finitely Connected Domains

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Publisher
Springer Journals
Copyright
Copyright © 2014 by Springer-Verlag Berlin Heidelberg
Subject
Mathematics; Analysis; Computational Mathematics and Numerical Analysis; Functions of a Complex Variable
ISSN
1617-9447
eISSN
2195-3724
DOI
10.1007/s40315-014-0056-0
Publisher site
See Article on Publisher Site

Abstract

This paper is concerned with the study of quasi-extremal distance domains, a class of domains introduced by Gehring and Martio in connection with the theory of quasiconformal mappings. We obtain a sharp upper bound for the quasi-extremal distance constant $$M(\Omega )$$ M ( Ω ) of a finitely connected planar domain in terms of local boundary dilatation of its boundary components. For the proof of the main theorem, several independently interesting results are also established. One of them is a decomposition lemma about the extremal length of a curve family.

Journal

Computational Methods and Function TheorySpringer Journals

Published: Mar 5, 2014

References