Creating and Flattening Cusp Singularities by Deformations of Bi-conformal Energy

Research output: Contribution to journalArticle

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.

Original languageEnglish (US)
JournalJournal of Geometric Analysis
DOIs
StateAccepted/In press - Jan 1 2020

Keywords

  • Bi-conformal energy
  • Cusp
  • Mappings of integrable distortion
  • quasiball

ASJC Scopus subject areas

  • Geometry and Topology

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