arXiv:1908.10612v6 [math.DG] 8 Jul 2021 Page 1 arXiv:1908.10612v6 [math.DG] 8 Jul 2021
Four Lectures on Scalar Curvature Misha Gromov July 9, 2021 Unlike manifolds with controlled …

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 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 …

In this paper we consider metric fillings of boundaries of convex bodies. We show that
convex bodies are the unique minimal fillings of their boundary metrics among all integral …

We show that in the setting of proper metric spaces one obtains a solution of the classical 2-
dimensional Plateau problem by minimizing the energy, as in the classical case, once a …

We prove that every Riemannian metric on the 2-disc such that all its geodesics are minimal
is a minimal filling of its boundary (within the class of fillings homeomorphic to the disc). This …

We study isometric embeddings of a Euclidean space or a Heisenberg group into a higher
dimensional Heisenberg group, where both the source and target space are equipped with …

arXiv:2302.07587v1 [math.DG] 15 Feb 2023 Page 1 arXiv:2302.07587v1 [math.DG] 15 Feb
2023 LIPSCHITZ RIGIDIGY OF LIPSCHITZ MANIFOLDS AMONG INTEGRAL CURRENT …

We give a characterization of metric space-valued Sobolev maps in terms of weak*
derivatives. More precisely, we show that Sobolev maps with values in dual-to-separable …

This paper is a continuation of our paper about boundary rigidity and filling minimality of
metrics close to flat ones. We show that compact regions close to a hyperbolic one are …