Maximal metric surfaces and the Sobolev-to-Lipschitz property
Metric Geometry
2020-02-11 v2 Complex Variables
Differential Geometry
Abstract
We find maximal representatives within equivalence classes of metric spheres. For Ahlfors regular spheres these are uniquely characterized by satisfying the seemingly unrelated notions of Sobolev-to-Lipschitz property, or volume rigidity. We also apply our construction to solutions of the Plateau problem in metric spaces and obtain a variant of the associated intrinsic disc studied by Lytchak--Wenger, which satisfies a related maximality condition.
Keywords
Cite
@article{arxiv.1909.10385,
title = {Maximal metric surfaces and the Sobolev-to-Lipschitz property},
author = {Paul Creutz and Elefterios Soultanis},
journal= {arXiv preprint arXiv:1909.10385},
year = {2020}
}
Comments
33 pages