Creutz, Paul Soultanis, Elefterios 2020-09-20 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. application/pdf https://folia.unifr.ch/global/documents/309202 https://folia.unifr.ch/documents/309202/files/sul_mms.pdf eng info:eu-repo/semantics/altIdentifier/doi/10.1007/s00526-020-01843-0 info:eu-repo/semantics/openAccess License undefined Calculus of Variations and Partial Differential Equations. - 2020, vol. 59, no. 5, p. 177 info:eu-repo/classification/udc/51 Maximal metric surfaces and the Sobolev-to-Lipschitz property http://purl.org/coar/resource_type/c_6501