@article{6de1e15e93464978a4e8fe157c1ed066,
title = "A construction of trivial beltrami coefficients",
abstract = " A measurable function μ on the unit disk D of the complex plane with ‖μ‖ ∞ < 1 is sometimes called a Beltrami coefficient. We say that μ is trivial if it is the complex dilatation (Formula Presented) of a quasiconformal automorphism f of D satisfying the trivial boundary condition f (z) = z, |z| = 1. Since it is not easy to solve the Beltrami equation explicitly, to detect triviality of a given Beltrami coefficient is a hard problem, in general. In the present article, we offer a sufficient condition for a Beltrami coefficient to be trivial. Our proof is based on Betker{\textquoteright}s theorem on L{\"o}wner chains. ",
keywords = "L{\"o}wner chain, Quasiconformal mapping, Universal teichm{\"u}ller space",
author = "Toshiyuki Sugawa",
note = "Funding Information: Received by the editors April 19, 2017, and, in revised form, September 14, 2017. 2010 Mathematics Subject Classification. Primary 30C62; Secondary 30C55, 30F60. Key words and phrases. L{\"o}wner chain, quasiconformal mapping, universal Teichm{\"u}ller space. The present work was supported in part by JSPS KAKENHI Grant Number JP15K13441. Publisher Copyright: {\textcopyright} 2018 American Mathematical Society.",
year = "2019",
month = feb,
doi = "10.1090/proc/13965",
language = "English",
volume = "147",
pages = "629--635",
journal = "Proceedings of the American Mathematical Society",
issn = "0002-9939",
publisher = "American Mathematical Society",
number = "2",
}