## Abstract

The paper establishes the existence of homeomorphisms between two planar domains that minimize the Dirichlet energy. Among all homeomorphisms, between bounded doubly connected domains such that Mod Ω≤Mod Ω^{*}there exists, unique up to conformal authomorphisms of Ω, an energy-minimal diffeomorphism. Here Mod stands for the conformal modulus of a domain. No boundary conditions are imposed on f. Although any energy-minimal diffeomorphism is harmonic, our results underline the major difference between the existence of harmonic diffeomorphisms and the existence of the energy-minimal diffeomorphisms. The existence of globally invertible energy-minimal mappings is of primary pursuit in the mathematical models of nonlinear elasticity and is also of interest in computer graphics.

Original language | English (US) |
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Pages (from-to) | 667-707 |

Number of pages | 41 |

Journal | Inventiones Mathematicae |

Volume | 186 |

Issue number | 3 |

DOIs | |

State | Published - Dec 2011 |

## ASJC Scopus subject areas

- Mathematics(all)