Maximal metric surfaces and the Sobolev-to-Lipschitz property

  title={Maximal metric surfaces and the Sobolev-to-Lipschitz property},
  author={Paul Creutz and Elefterios Soultanis},
  journal={arXiv: Metric Geometry},
  • Paul Creutz, Elefterios Soultanis
  • Published 2019
  • Mathematics
  • arXiv: Metric Geometry
  • 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. 
    3 Citations


    Canonical parametrizations of metric discs
    • 13
    • PDF
    Space of minimal discs and its compactification
    • 4
    • PDF
    Quasisymmetric parametrizations of two-dimensional metric spheres
    • 137
    • PDF
    Uniformization Of Metric Surfaces Using Isothermal Coordinates
    • 6
    • PDF
    Energy and area minimizers in metric spaces
    • 13
    • PDF
    Area Minimizing Discs in Metric Spaces
    • 33
    • PDF
    Intrinsic structure of minimal discs in metric spaces
    • 19
    • Highly Influential
    • PDF
    Lipschitz-Volume rigidity on limit spaces with Ricci curvature bounded from below
    • 5
    • PDF