Regularity of harmonic discs in spaces with quadratic isoperimetric inequality

2015/12/03 by Alexander Lytchak, Stefan Wenger, Lytchak, Alexander +1 · 1 citation
Mathematics · #Geometric Analysis and Curvature Flows #Nonlinear Partial Differential Equations #Numerical methods in inverse problems #math.AP #math.MG #msc:58E20

paper · pdf · doi:10.48550/arxiv.1512.01060

arxiv created 2015/12/03 · arxiv updated 2015/12/04

Abstract

We study harmonic and quasi-harmonic discs in metric spaces admitting a uniformly local quadratic isoperimetric inequality for curves. The class of such metric spaces includes compact Lipschitz manifolds, metric spaces with upper or lower curvature bounds in the sense of Alexandrov, some sub-Riemannian manifolds, and many more. In this setting, we prove local Hoelder continuity and continuity up to the boundary of harmonic and quasi-harmonic discs.

Cited by

• Uniformization of metric surfaces: A survey

Related

• Rigidity of the Pu inequality and quadratic isoperimetric constants of normed spaces
• Intrinsic structure of minimal discs in metric spaces
• Isoperimetric characterization of upper curvature bounds
• Space of minimal discs and its compactification
• Majorization by Hemispheres & Quadratic Isoperimetric Constants