Lipschitz property of minimisers between double connected surfaces

2019/02/11 by Kalaj, David
#Complex Variables (math.CV) #FOS: Mathematics

paper · doi:10.48550/arxiv.1902.04167

Abstract

We study the global Lipschitz character of minimisers of the Dirichlet energy of diffeomorphisms between doubly connected domains with smooth boundaries from Riemann surfaces. The key point of the proof is the fact that minimisers are certain Noether harmonic maps, with Hopf differential of special form, a fact invented by Iwaniec, Koh, Kovalev and Onninen in \citeinv for Euclidean metric and by the author in \citecalculus for the arbitrary metric, which depends deeply on a result of Jost \citeJob1.

Related

• Lipschitz regularity of energy-minimal mappings between doubly connected Riemann surfaces
• Kellogg's theorem for diffeomophic minimisers of Dirichlet energy\n between doubly connected Riemann surfaces
• Energy-minimal diffeomorphisms between doubly connected Riemann surfaces
• Minimisers and Kellogg's theorem
• Stability of Minimising Harmonic Maps under W^1,p Perturbations of Boundary Data: p≥ 2