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A symplectic functional analytic proof of the conformal welding theorem
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Analysis and Probability Theory.
2015 (English)In: Proceedings of the American Mathematical Society, ISSN 0002-9939, E-ISSN 1088-6826, Vol. 143, no 1, 265-278 p.Article in journal (Refereed) Published
Abstract [en]

We give a new functional-analytic/symplectic geometric proof of the conformal welding theorem. This is accomplished by representing composition by a quasisymmetric map phi as an operator on a suitable Hilbert space and algebraically solving the conformal welding equation for the unknown maps f and g satisfying g o phi = f. The univalence and quasiconformal extendibility of f and g is demonstrated through the use of the Grunsky matrix.

Place, publisher, year, edition, pages
2015. Vol. 143, no 1, 265-278 p.
Keyword [en]
Conformal welding, Grunsky matrix, infinite Siegel disk, quasi-symmetries, conformal maps
National Category
Mathematics
Identifiers
URN: urn:nbn:se:uu:diva-251861DOI: 10.1090/S0002-9939-2014-12225-8ISI: 000351490000028OAI: oai:DiVA.org:uu-251861DiVA: diva2:807827
Available from: 2015-04-24 Created: 2015-04-24 Last updated: 2017-12-04Bibliographically approved

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Staubach, Wolfgang

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