A symplectic functional analytic proof of the conformal welding theorem
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
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.
Conformal welding, Grunsky matrix, infinite Siegel disk, quasi-symmetries, conformal maps
IdentifiersURN: urn:nbn:se:uu:diva-251861DOI: 10.1090/S0002-9939-2014-12225-8ISI: 000351490000028OAI: oai:DiVA.org:uu-251861DiVA: diva2:807827