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arXiv · 1512.01060

Regularity of harmonic discs in spaces with quadratic isoperimetric inequality

Alexander Lytchak·Stefan Wenger
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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.

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Alexander Lytchak, Stefan Wenger. 2015-12-03. Regularity of harmonic discs in spaces with quadratic isoperimetric inequality. https://arxiv.org/abs/1512.01060

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