Tadeusz Iwaniec and Jani Onninen
Abstract: 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.
Journal: Bulletin London Mathematical Society Volume 46 (2014), Issue 6, 1283-1291.
DOI: 10.1112/blms/bdu084