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September 2010 Existence of extremal Beltrami coefficients with nonconstant modulus
Guowu Yao
Nagoya Math. J. 199: 1-14 (September 2010). DOI: 10.1215/00277630-2010-001

Abstract

Suppose that [μ]T(Δ) is a point of the universal Teichmüller space T(Δ). In 1998, Božin, Lakic, Marković, and Mateljević showed that there exists μ such that μ is uniquely extremal in [μ]T(Δ) and has a nonconstant modulus. It is a natural problem whether there is always an extremal Beltrami coefficient of constant modulus in [μ]T(Δ) if [μ]T(Δ) admits infinitely many extremal Beltrami coefficients; the purpose of this paper is to show that the answer is negative. An infinitesimal version is also obtained. Extremal sets of extremal Beltrami coefficients are considered, and an open problem is proposed. The key tool of our argument is Reich’s construction theorem.

Citation

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Guowu Yao. "Existence of extremal Beltrami coefficients with nonconstant modulus." Nagoya Math. J. 199 1 - 14, September 2010. https://doi.org/10.1215/00277630-2010-001

Information

Published: September 2010
First available in Project Euclid: 14 September 2010

zbMATH: 1227.30021
MathSciNet: MR2730409
Digital Object Identifier: 10.1215/00277630-2010-001

Subjects:
Primary: 30C75
Secondary: 30C62

Rights: Copyright © 2010 Editorial Board, Nagoya Mathematical Journal

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Vol.199 • September 2010
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