## 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.

Original language | English (US) |
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Pages (from-to) | 1283-1291 |

Number of pages | 9 |

Journal | Bulletin of the London Mathematical Society |

Volume | 46 |

Issue number | 6 |

DOIs | |

State | Published - Dec 1 2014 |

## ASJC Scopus subject areas

- Mathematics(all)