Radó-Kneser-Choquet theorem

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14 Scopus citations


We present a new approach to the celebrated theorem of Radó-Kneser-Choquet (RKC) on univalence of planar harmonic mappings. The novelty lies in establishing a continuous path (isotopy) from the given harmonic map to a conformal one. Along this path the mappings retain positive Jacobian determinant by virtue of so-called Minimum Principle. These ideas extend to nonlinear uncoupled systems of partial differential equations, as in Iwaniec, Koski and Onninen ['Isotropic $p$-harmonic systems in 2D, Jacobian estimates and univalent solutions', Rev. Mat. Iberoam, to appear]. Unfortunately, details of such digression would lead us too far afield. Nonetheless, one gains (in particular) the RKC-Theorem for the isotropic $p$-harmonic deformations.

Original languageEnglish (US)
Pages (from-to)1283-1291
Number of pages9
JournalBulletin of the London Mathematical Society
Issue number6
StatePublished - Dec 1 2014

ASJC Scopus subject areas

  • General Mathematics


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