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 …

We prove that any length metric space homeomorphic to a 2-manifold with boundary, also
called a length surface, is the Gromov–Hausdorff limit of polyhedral surfaces with controlled …

We prove that any metric surface (that is, metric space homeomorphic to a 2-manifold with
boundary) with locally finite Hausdorff 2-measure is the Gromov–Hausdorff limit of …

We use the recently established existence and regularity of area and energy minimizing
disks in metric spaces to obtain canonical parameterizations of metric surfaces. Our …

We study the intrinsic structure of parametric minimal discs in metric spaces admitting a
quadratic isoperimetric inequality. We associate to each minimal disc a compact, geodesic …

We look for minimal conditions on a two-dimensional metric surface X of locally finite
Hausdorff 2-measure under which X admits an (almost) parametrization with good geometric …

We find maximal representatives within equivalence classes of metric spheres. For Ahlfors
regular spheres these are uniquely characterized by satisfying the seemingly unrelated …

Abstract The Plateau–Douglas problem asks to find an area minimizing surface of fixed or
bounded genus spanning a given finite collection of Jordan curves in Euclidean space. In …

We establish the following uniformization result for metric spaces $ X $ of finite Hausdorff 2-
measure. If $ X $ is homeomorphic to a smooth 2-manifold $ M $ with non-empty boundary …

Let $ X $ be a Banach space or more generally a complete metric space admitting a conical
geodesic bicombing. We prove that every closed $ L $-Lipschitz curve $\gamma: S …