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 editorsIwaniec, Tadeusz; Onninen, Jani; Zhu, Zheng

Journal or seriesJournal of Geometric Analysis



Publication year2021


Issue number3

Pages range2331-2353


Publication countryUnited States

Publication languageEnglish


Publication open accessNot open

Publication channel open access

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


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.


Free keywordscusp; bi-conformal energy; mappings of integrable distortion; quasiball

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Ministry reportingYes

Reporting Year2021

JUFO rating2

Last updated on 2024-03-04 at 21:16