Bilipschitz and quasiconformal rotation, stretching and multifractal spectra

Kari Astala; Tadeusz Iwaniec; István Prause; Eero Saksman

doi:10.1007/s10240-014-0065-6

Bilipschitz and quasiconformal rotation, stretching and multifractal spectra

Kari Astala, Tadeusz Iwaniec, István Prause, Eero Saksman

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

20 Scopus citations

Abstract

We establish sharp bounds for simultaneous local rotation and Hölder-distortion of planar quasiconformal maps. In addition, we give sharp estimates for the corresponding joint quasiconformal multifractal spectrum, based on new estimates for Burkholder functionals with complex parameters. As a consequence, we obtain optimal rotation estimates also for bi-Lipschitz maps.

Original language	English (US)
Pages (from-to)	113-154
Number of pages	42
Journal	Publications Mathematiques de l'Institut des Hautes Etudes Scientifiques
Volume	121
Issue number	1
DOIs	https://doi.org/10.1007/s10240-014-0065-6
State	Published - Jun 27 2015

ASJC Scopus subject areas

General Mathematics

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title = "Bilipschitz and quasiconformal rotation, stretching and multifractal spectra",

abstract = "We establish sharp bounds for simultaneous local rotation and H{\"o}lder-distortion of planar quasiconformal maps. In addition, we give sharp estimates for the corresponding joint quasiconformal multifractal spectrum, based on new estimates for Burkholder functionals with complex parameters. As a consequence, we obtain optimal rotation estimates also for bi-Lipschitz maps.",

author = "Kari Astala and Tadeusz Iwaniec and Istv{\'a}n Prause and Eero Saksman",

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AU - Prause, István

AU - Saksman, Eero

PY - 2015/6/27

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AB - We establish sharp bounds for simultaneous local rotation and Hölder-distortion of planar quasiconformal maps. In addition, we give sharp estimates for the corresponding joint quasiconformal multifractal spectrum, based on new estimates for Burkholder functionals with complex parameters. As a consequence, we obtain optimal rotation estimates also for bi-Lipschitz maps.

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Bilipschitz and quasiconformal rotation, stretching and multifractal spectra

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