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 et al. (Invent Math 186:667–707, 2011) for Euclidean metric and by the author in Kalaj (Calc Var Partial Differ Equ 51:465–494, 2014) for the arbitrary metric, which depends deeply on a result of Jost (in: Yau (ed) Tsing Hua lectures on geometry and analysis, Taiwan, 1990–91. International Press, Cambridge, 1997).
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
