2010/08/03 by Tadeusz Iwaniec, Ngin-Tee Koh, Leonid V. Kovalev +1 · 1 citation
Mathematics · #math.CV #msc:58E20 #msc:30C62 #msc:31A05
paper · pdf · doi:10.1007/s00222-011-0327-6
published as Invent. Math. 186 (2011), no. 3, 667-707 · 34 pages, no figures
arxiv created 2010/08/03 · arxiv updated 2011/12/16
The paper establishes the existence of homeomorphisms between two planar domains that minimize the Dirichlet energy. Specifically, among all homeomorphisms f : R -> R* between bounded doubly connected domains such that Mod (R) < Mod (R*) there exists, unique up to conformal authomorphisms of R, an energy-minimal diffeomorphism. 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.