Rotation Bounds for Hölder Continuous Homeomorphisms with Integrable Distortion

A. Clop; L. Hitruhin; B. Sengupta

doi:10.1007/s12220-022-00950-y

Rotation Bounds for Hölder Continuous Homeomorphisms with Integrable Distortion

A. Clop^*, L. Hitruhin, B. Sengupta

^*Corresponding author for this work

Department of Mathematics and Systems Analysis

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

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Abstract

We obtain sharp rotation bounds for the subclass of homeomorphisms f: C→ C of finite distortion which have distortion function in Llocp, p> 1 , and for which a Hölder continuous inverse is available. The interest in this class is partially motivated by examples arising from fluid mechanics. Our rotation bounds hereby presented improve the existing ones, for which the Hölder continuity is not assumed. We also present examples proving sharpness.

Original language	English
Article number	212
Pages (from-to)	1-21
Number of pages	21
Journal	JOURNAL OF GEOMETRIC ANALYSIS
Volume	32
Issue number	8
DOIs	https://doi.org/10.1007/s12220-022-00950-y
Publication status	Published - Aug 2022
MoE publication type	A1 Journal article-refereed

Keywords

Mappings of finite distortion
Quasiconformal maps
Rotation bounds

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10.1007/s12220-022-00950-y

Rotation Bounds for Hölder Continuous Homeomorphisms with Integrable DistortionFinal published version, 283 KBLicence: CC BY

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@article{197b2e460ac64e06b17df6ba7e6c90eb,

title = "Rotation Bounds for H{\"o}lder Continuous Homeomorphisms with Integrable Distortion",

abstract = "We obtain sharp rotation bounds for the subclass of homeomorphisms f: C→ C of finite distortion which have distortion function in Llocp, p> 1 , and for which a H{\"o}lder continuous inverse is available. The interest in this class is partially motivated by examples arising from fluid mechanics. Our rotation bounds hereby presented improve the existing ones, for which the H{\"o}lder continuity is not assumed. We also present examples proving sharpness.",

keywords = "Mappings of finite distortion, Quasiconformal maps, Rotation bounds",

author = "A. Clop and L. Hitruhin and B. Sengupta",

note = "| openaire: EC/H2020/834728/EU//QUAMAP Funding Information A.C. and B.S. are partially supported by projects MTM2016-81703-ERC, MTM2016-75390 (Spanish Government) and 2017SGR395 (Catalan Government). L.H. was partially supported by ICMAT Severo Ochoa project SEV-2015-0554 grant MTM2017-85934-C3-2-P, the ERC grant 307179-GFTIPFD, the ERC grant 834728 Quamap, by the Finnish Academy of Science project 13316965 and by a grant from The Emil Aaltonen Foundation. Publisher Copyright: {\textcopyright} 2022, The Author(s).",

year = "2022",

month = aug,

doi = "10.1007/s12220-022-00950-y",

language = "English",

volume = "32",

pages = "1--21",

journal = "JOURNAL OF GEOMETRIC ANALYSIS",

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T1 - Rotation Bounds for Hölder Continuous Homeomorphisms with Integrable Distortion

AU - Clop, A.

AU - Hitruhin, L.

AU - Sengupta, B.

N1 - | openaire: EC/H2020/834728/EU//QUAMAP Funding Information A.C. and B.S. are partially supported by projects MTM2016-81703-ERC, MTM2016-75390 (Spanish Government) and 2017SGR395 (Catalan Government). L.H. was partially supported by ICMAT Severo Ochoa project SEV-2015-0554 grant MTM2017-85934-C3-2-P, the ERC grant 307179-GFTIPFD, the ERC grant 834728 Quamap, by the Finnish Academy of Science project 13316965 and by a grant from The Emil Aaltonen Foundation. Publisher Copyright: © 2022, The Author(s).

PY - 2022/8

Y1 - 2022/8

N2 - We obtain sharp rotation bounds for the subclass of homeomorphisms f: C→ C of finite distortion which have distortion function in Llocp, p> 1 , and for which a Hölder continuous inverse is available. The interest in this class is partially motivated by examples arising from fluid mechanics. Our rotation bounds hereby presented improve the existing ones, for which the Hölder continuity is not assumed. We also present examples proving sharpness.

AB - We obtain sharp rotation bounds for the subclass of homeomorphisms f: C→ C of finite distortion which have distortion function in Llocp, p> 1 , and for which a Hölder continuous inverse is available. The interest in this class is partially motivated by examples arising from fluid mechanics. Our rotation bounds hereby presented improve the existing ones, for which the Hölder continuity is not assumed. We also present examples proving sharpness.

KW - Mappings of finite distortion

KW - Quasiconformal maps

KW - Rotation bounds

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U2 - 10.1007/s12220-022-00950-y

DO - 10.1007/s12220-022-00950-y

M3 - Article

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JF - JOURNAL OF GEOMETRIC ANALYSIS

IS - 8

M1 - 212

ER -

Rotation Bounds for Hölder Continuous Homeomorphisms with Integrable Distortion

Abstract

Keywords

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QUAMAP: Quasiconformal Methods in Analysis and Applications

Geometric Analysis and Conformal Structures

Cite this

Rotation Bounds for Hölder Continuous Homeomorphisms with Integrable Distortion

Abstract

Keywords

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Other files and links

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Projects

QUAMAP: Quasiconformal Methods in Analysis and Applications

Geometric Analysis and Conformal Structures

Cite this