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Main Title: The Loewner equation and Lipschitz graphs
Author(s): Rohde, Steffen
Tran, Huy
Zinsmeister, Michel
Type: Article
Language Code: en
Abstract: The proofs of continuity of Loewner traces in the stochastic and in the deterministic settings employ different techniques. In the former setting of the Schramm–Loewner evolution SLE, Hölder continuity of the conformal maps is shown by estimating the derivatives, whereas the latter setting uses the theory of quasiconformal maps. In this note, we adopt the former method to the deterministic setting and obtain a new and elementary proof that Hölder-1/2 driving functions with norm less than 4 generate simple arcs. We also give a sufficient condition for driving functions to generate curves that are graphs of Lipschitz functions.
Issue Date: 2018
Date Available: 31-Jan-2019
DDC Class: 510 Mathematik
Subject(s): Loewner differential equation
Sponsor/Funder: NSF, DMS-1068105, Loewner Evolutions and Random Maps
Journal Title: Revista matemática iberoamericana
Publisher: European Mathematical Society
Publisher Place: Zürich
Volume: 34
Issue: 2
Publisher DOI: 10.4171/RMI/1010
Page Start: 937
Page End: 948
ISSN: 0213-2230
Notes: Dieser Beitrag ist mit Zustimmung des Rechteinhabers aufgrund einer (DFG geförderten) Allianz- bzw. Nationallizenz frei zugänglich.
This publication is with permission of the rights owner freely accessible due to an Alliance licence and a national licence (funded by the DFG, German Research Foundation) respectively.
Appears in Collections:Inst. Mathematik » Publications

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