Get 20M+ Full-Text Papers For Less Than $1.50/day. Start a 14-Day Trial for You or Your Team.

Learn More →

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

Download PDF
16 pages

Loading next page...
 
/lp/springer-journals/extremal-length-decomposition-and-domain-constants-for-finitely-iMa5JIqWG0
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 Theory – Springer Journals

Published: Mar 5, 2014

References

  • Lectures on Quasiconformal Mappings. Van Nostrand Mathematical studies
    Ahlfors, LV
  • Conformal Invariants
    Ahlfors, LV
  • Functions of One Complex Variable II
    Conway, JB
  • Some properties of the reduced inner modulus
    Dubinin, VN
  • Quasiextremal distance domains and integrability of derivatives of conformal mappings
    Garnett, JB; Yang, S
  • Quasiextremal distance domains and extension of quasiconformal mappings
    Gehring, FW; Martio, O
  • Univalent Functions and Conformal Mappings
    Jenkins, JA
  • Conformal invariants of QED domains
    Shen, Y
  • QED domains and NED sets in $$\overline{\mathbb{R}}^n$$ R ¯ n
    Yang, S
  • A modulus inequality for condensers and conformal invariants of smooth domains
    Yang, S