10 citations · 20 across the 22 of their papers we have counts for
14 papers · 1 filter
Infinitesimally Euclidean metric surfaces
Alexander Lytchak, Elefterios Soultanis
We prove the equivalence of several notions of infinitesimally Euclidean-like behaviour for metric surfaces appearing in the literature. We obtain in particular that metric surface…
Embeddability and rectifiability of Lipschitz differentiability spaces
Ivan Caamano, Sylvester Eriksson-Bique, Elefterios Soultanis
We prove that Lipschitz differentiability spaces which bi-Lipschitz embed into an RNP-space are countably rectifiable. In contrast to earlier methods of Cheeger and Kleiner, our ap…
Limits of mapping packages and tangents of Sobolev maps
Milica Caković, Elefterios Soultanis
We show the existence of ultralimits of sequences of Hajlasz-Sobolev mappings when converges to a limit space in the pointed measured Gromov (pmG) sense, par…
Spaces with Riemannian curvature bounds are universally infinitesimally Hilbertian
Jesús Núñez-Zimbrón, Enrico Pasqualetto, Elefterios Soultanis
We show that a metric space that, at every point, has a Gromov-Hausdorff tangent with the splitting property (i.e. every geodesic line splits off a factor ), is uni…
Characterization of metric spaces with a metric fundamental class
Denis Marti, Elefterios Soultanis
We consider three conditions on metric manifolds with finite volume: (1) the existence of a metric fundamental class, (2) local index bounds for Lipschitz maps, and (3) Gromov--Hau…
Connections between metric differentiability and rectifiability
Iván Caamaño, Estíbalitz Durand-Cartagena, Jesús Á. Jaramillo +2
We combine Kirchheim's metric differentials with Cheeger charts in order to establish a non-embeddability principle for any collection of Banach (or metric) spaces: if…
A non-compact convex hull in generalized non-positive curvature
Giuliano Basso, Yannick Krifka, Elefterios Soultanis
In this article, we are interested in metric spaces that satisfy a weak non-positive curvature condition in the sense that they admit a conical geodesic bicombing. We show that the…
Curvewise characterizations of minimal upper gradients and the construction of a Sobolev differential
Sylvester Eriksson-Bique, Elefterios Soultanis
We represent minimal upper gradients of Newtonian functions, in the range , by maximal directional derivatives along "generic" curves passing through a given point,…
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…
Pull-back of metric currents and homological boundedness of BLD-elliptic spaces
Pekka Pankka, Elefterios Soultanis
Using the duality of metric currents and polylipschitz forms, we show that a BLD-mapping between oriented cohomology manifolds and induces a pull-back oper…
Homotopy classes of Newtonian spaces
Elefterios Soultanis
We study notions of homotopy in the Newtonian space of Sobolev type maps between metric spaces. After studying the properties and relations of two different notions…