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Spiraling Minimal Graphs

Spiraling Minimal Graphs We consider minimal graphs $$\ u=u(x,y)>0$$ u = u ( x , y ) > 0 over unbounded spiraling domains D with $$\ u=0$$ u = 0 on $$\partial D$$ ∂ D . We show that such surfaces do exist, but only if the rate of spiraling is restricted. Restrictions are obtained through the method of extremal length of path families, and constructions are achieved by means of quasiconformal mappings. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Computational Methods and Function Theory Springer Journals

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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/s40315-014-0069-8
Publisher site
See Article on Publisher Site

Abstract

We consider minimal graphs $$\ u=u(x,y)>0$$ u = u ( x , y ) > 0 over unbounded spiraling domains D with $$\ u=0$$ u = 0 on $$\partial D$$ ∂ D . We show that such surfaces do exist, but only if the rate of spiraling is restricted. Restrictions are obtained through the method of extremal length of path families, and constructions are achieved by means of quasiconformal mappings.

Journal

Computational Methods and Function TheorySpringer Journals

Published: May 6, 2014

References