9 papers
Tensorization of quasi-Hilbertian Sobolev spaces
Sylvester Eriksson-Bique, Tapio Rajala, Elefterios Soultanis
The tensorization problem for Sobolev spaces asks for a characterization of how the Sobolev space on a product metric measure space can be determined from its factors.…
Area minimizing surfaces in homotopy classes in metric spaces
Elefterios Soultanis, Stefan Wenger
We introduce and study a notion of relative 1-homotopy type for Sobolev maps from a surface to a metric space spanning a given collection of Jordan curves. We use this to establish…
Abstract and concrete tangent modules on Lipschitz differentiability spaces
Toni Ikonen, Enrico Pasqualetto, Elefterios Soultanis
We construct an isometric embedding from Gigli's abstract tangent module into the concrete tangent module of a space admitting a (weak) Lipschitz differentiable structure, and give…
Maximal metric surfaces and the Sobolev-to-Lipschitz property
Paul Creutz, Elefterios Soultanis
We find maximal representatives within equivalence classes of metric spheres. For Ahlfors regular spheres these are uniquely characterized by satisfying the seemingly unrelated not…
Metric currents and polylipschitz forms
Pekka Pankka, Elefterios Soultanis
We construct, for a locally compact metric space , a space of polylipschitz forms , which is a pre-dual for the space of metric currents of Ambr…
Infinitesimal Hilbertianity of locally CAT()-spaces
Simone Di Marino, Nicola Gigli, Enrico Pasqualetto +1
We show that, given a metric space of curvature bounded from above in the sense of Alexandrov, and a positive Radon measure on giving finite mass to bounded sets, t…