Lytchak, Alexander Wenger, Stefan 2017-03-01 We solve the classical problem of Plateau in the setting of proper metric spaces. Precisely, we prove that among all disc-type surfaces with prescribed Jordan boundary in a proper metric space there exists an area minimizing disc which moreover has a quasi-conformal parametrization. If the space supports a local quadratic isoperimetric inequality for curves we prove that such a solution is locally Hölder continuous in the interior and continuous up to the boundary. Our results generalize corresponding results of Douglas Radò and Morrey from the setting of Euclidean space and Riemannian manifolds to that of proper metric spaces. application/pdf https://folia.unifr.ch/global/documents/305458 https://folia.unifr.ch/documents/305458/files/wen_amd.pdf eng info:eu-repo/semantics/altIdentifier/doi/10.1007/s00205-016-1054-3 info:eu-repo/semantics/openAccess License undefined Archive for Rational Mechanics and Analysis. - 2017, vol. 223, no. 3, p. 1123–1182 info:eu-repo/classification/udc/51 Area minimizing discs in metric spaces http://purl.org/coar/resource_type/c_6501