The Loewner equation and Lipschitz graphs
| dc.contributor.author | Rohde, Steffen | |
| dc.contributor.author | Tran, Huy | |
| dc.contributor.author | Zinsmeister, Michel | |
| dc.date.accessioned | 2019-01-31T10:40:22Z | |
| dc.date.available | 2019-01-31T10:40:22Z | |
| dc.date.issued | 2018 | |
| dc.description | Dieser Beitrag ist mit Zustimmung des Rechteinhabers aufgrund einer (DFG geförderten) Allianz- bzw. Nationallizenz frei zugänglich. | de |
| dc.description | 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. | en |
| dc.description.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. | en |
| dc.description.sponsorship | NSF, DMS-1068105, Loewner Evolutions and Random Maps | en |
| dc.identifier.issn | 0213-2230 | |
| dc.identifier.uri | https://depositonce.tu-berlin.de/handle/11303/9054 | |
| dc.identifier.uri | http://dx.doi.org/10.14279/depositonce-8155 | |
| dc.language.iso | en | en |
| dc.rights.uri | http://rightsstatements.org/vocab/InC/1.0/ | en |
| dc.subject.ddc | 510 Mathematik | de |
| dc.subject.other | Loewner differential equation | en |
| dc.title | The Loewner equation and Lipschitz graphs | en |
| dc.type | Article | en |
| dc.type.version | publishedVersion | en |
| dcterms.bibliographicCitation.doi | 10.4171/RMI/1010 | en |
| dcterms.bibliographicCitation.issue | 2 | en |
| dcterms.bibliographicCitation.journaltitle | Revista matemática iberoamericana | en |
| dcterms.bibliographicCitation.originalpublishername | European Mathematical Society | en |
| dcterms.bibliographicCitation.originalpublisherplace | Zürich | en |
| dcterms.bibliographicCitation.pageend | 948 | en |
| dcterms.bibliographicCitation.pagestart | 937 | en |
| dcterms.bibliographicCitation.volume | 34 | en |
| tub.accessrights.dnb | domain | en |
| tub.affiliation | Fak. 2 Mathematik und Naturwissenschaften::Inst. Mathematik | de |
| tub.affiliation.faculty | Fak. 2 Mathematik und Naturwissenschaften | de |
| tub.affiliation.institute | Inst. Mathematik | de |
| tub.publisher.universityorinstitution | Technische Universität Berlin | en |