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 …

Ricci curvature in dimension 2 Page 1 © 2022 European Mathematical Society Published by
EMS Press and licensed under a CC BY 4.0 license J. Eur. Math. Soc. 25, 845–867 (2023) DOI …

For an intergral $2 $-varifold $ V=\underline {v}(\Sigma,\theta_ {\ge 1}) $ in the unit ball $
B_1 $ passing through the original point, assuming the critical Allard condition holds, that is …

We solve the classical problem of Plateau in every metric space which is $1 $-
complemented in an ultra-completion of itself. This includes all proper metric spaces as well …

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

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The Dehn function measures the area of minimal discs that fill closed curves in a space; it is
an important invariant in analysis, geometry, and geometric group theory. There are several …

We prove that a Sobolev map from a Riemannian manifold into a complete metric space
pushes forward almost every compactly supported integral current to an Ambrosio …