Document Type
Article
Date
2-15-2010
Disciplines
Mathematics
Description/Abstract
The concept of a conformal deformation has two natural extensions: quasiconformal and harmonic mappings. Both classes do not preserve the conformal type of the domain, however they cannot change it in an arbitrary way. Doubly connected domains are where one first observes nontrivial conformal invariants. Herbert Groetzsch and Johannes C. C. Nitsche addressed this issue for quasiconformal and harmonic mappings, respectively. Combining these concepts we obtain sharp estimates for quasiconformal harmonic mappings between doubly connected domains. We then apply our results to the Cauchy problem for minimal surfaces, also known as the Bjorling problem. Specifically, we obtain a sharp estimate of the modulus of a doubly connected minimal surface that evolves from its inner boundary with a given initial slope.
Recommended Citation
Iwaniec, Tadeusz; Kovalev, Leonid V.; and Onninen, Jani, "Doubly Connected Minimal Surfaces and Extremal Harmonic Mappings" (2010). Mathematics - All Scholarship. 62.
https://surface.syr.edu/mat/62
Source
Harvested from arXiv.org
Creative Commons License
This work is licensed under a Creative Commons Attribution 3.0 License.
Additional Information
This manuscript is from arXiv.org, for more information http://arxiv.org/abs/0912.3542