2011/08/03 by David Kalaj, Kalaj, David
Mathematics · #Analytic and geometric function theory #Complex Variables (math.CV) #Differential Geometry (math.DG) #FOS: Mathematics #math.CV #math.DG
paper · pdf · doi:10.48550/arxiv.1108.0773
32 pages. Some minor style changes appear in this version. arXiv admin note: text overlap with arXiv:1008.0652
openalex publication_date 2011/08/03 · arxiv created 2012/04/02 · arxiv updated 2012/04/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let N=(Ω,σ) and M=(Ω^*,ρ) be doubly connected Riemann surfaces and assume that ρ is a smooth metric with bounded Gauss curvature K and finite area. The paper establishes the existence of homeomorphisms between Ω and Ω^* that minimize the Dirichlet energy. In the class of all homeomorphisms f \colon Ω\onto Ω^∗ between doubly connected domains such that \Mod Ω≤ \Mod Ω^∗ there exists, unique up to conformal authomorphisms of Ω, an energy-minimal diffeomorphism which is a harmonic diffeomorphism. The results improve and extend some recent results of Iwaniec, Koh, Kovalev and Onninen (Inven. Math. (2011)), where the authors considered doubly connected domains in the complex plane w.r. to Euclidean metric.