Sewing homeomorphism and conformal invariants |
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| Authors: | Tao Cheng Hui Qiang Shi Shanshuang Yang |
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| Affiliation: | 1. Department of Mathematics, Shanghai Key Laboratory of Pure Mathematics and Mathematical Practice, East China Normal University, Shanghai 200241, P. R. China;2. Department of Mathematics and Computer Sciences, Emory University, Atlanta, GA 30322, USA;3. chool of Mathematics and Statistics, Hu'nan University of Commerce, Changsha 410205, P. R. China |
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| Abstract: | This paper is devoted to the study of some fundamental properties of the sewing homeomorphism induced by a Jordan domain. In particular, using conformal invariants such as harmonic measure, extremal distance, and reduced extremal distance, we give several necessary and sufficient conditions for the sewing homeomorphism to be bi-Lipschitz or bi-Hölder. Furthermore, equivalent conditions for a Jordan curve to be a quasicircle are also obtained. |
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| Keywords: | Bi-Lipschitz bi-Hö lder quasicircle modulus reduced extremal distance |
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