6533b7d2fe1ef96bd125e065
RESEARCH PRODUCT
Radó–Kneser–Choquet theorem
Tadeusz IwaniecJani Onninensubject
Pure mathematicsArzelà–Ascoli theoremFundamental theoremPicard–Lindelöf theoremGeneral MathematicsCompactness theoremta111Fixed-point theoremBrouwer fixed-point theoremSqueeze theoremMean value theoremMathematicsdescription
We present a new approach to the celebrated theorem of Rado–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.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2014-11-15 | Bulletin of the London Mathematical Society |