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 prove that a minimal disc in a CAT (0) space is a local embedding away from a finite set
of “branch points”. On the way we establish several basic properties of minimal surfaces …

We give a solution of Plateau's problem for singular curves possibly having self-
intersections. The proof is based on the solution of Plateau's problem for Jordan curves in …

We prove that upper curvature bounds in the sense of Alexandrov can be improved locally
by using appropriate conformal changes. As a new technical tool we derive a generalization …

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 …

Assume you are given a finite configuration Γ of disjoint rectifiable Jordan curves in R n. The
Plateau-Douglas problem asks whether there exists a minimizer of area among all compact …

The Dehn function of a metric space measures the area necessary in order to fill a closed
curve of controlled length by a disc. As a main result, we prove that a length space has …

In this paper, we survey the existence, uniqueness and interior regularity of solutions to the
Dirichlet problem associated with various energy functionals in the setting of mappings …

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