A1 Journal article (refereed)
Creating and Flattening Cusp Singularities by Deformations of Bi-conformal Energy (2021)

Iwaniec, T., Onninen, J., & Zhu, Z. (2021). Creating and Flattening Cusp Singularities by Deformations of Bi-conformal Energy. Journal of Geometric Analysis, 31(3), 2331-2353. https://doi.org/10.1007/s12220-019-00351-8

JYU authors or editors

Publication details

All authors or editors: Iwaniec, Tadeusz; Onninen, Jani; Zhu, Zheng

Journal or series: Journal of Geometric Analysis

ISSN: 1050-6926

eISSN: 1559-002X

Publication year: 2021

Volume: 31

Issue number: 3

Pages range: 2331-2353

Publisher: Springer

Publication country: United States

Publication language: English

DOI: https://doi.org/10.1007/s12220-019-00351-8

Publication open access: Not open

Publication channel open access: 

Web address of parallel published publication (pre-print): https://arxiv.org/abs/1907.06461

Abstract

Mappings of bi-conformal energy form the widest class of homeomorphisms that one can hope to build a viable extension of Geometric Function Theory with connections to mathematical models of Nonlinear Elasticity. Such mappings are exactly the ones with finite conformal energy and integrable inner distortion. It is in this way that our studies extend the applications of quasiconformal homeomorphisms to the degenerate elliptic systems of PDEs. The present paper searches a bi-conformal variant of the Riemann Mapping Theorem, focusing on domains with exemplary singular boundaries that are not quasiballs. We establish the sharp description of boundary singularities that can be created and flattened by mappings of bi-conformal energy.

Keywords: geometry

Free keywords: cusp; bi-conformal energy; mappings of integrable distortion; quasiball

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Related projects

Ministry reporting: Yes

Reporting Year: 2021

JUFO rating: 2