Elefterios Soultanis

activity

20132026

most citedCurvewise characterizations of minimal upper gradients and the construction of a Sobolev differential

10 citations · 20 across the 22 of their papers we have counts for

collaborators

28 papers

math.MG2026

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…

math.MG2026

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…

math.MG2026

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 $f_{i} : X_{i} \to Y_{i}$ when $X_{i}$ converges to a limit space in the pointed measured Gromov (pmG) sense, par…

math.DG2025

Pull-back of differential forms by multi-valued Sobolev maps, and the quasiregularity of the multi-valued inverse of a quasiregular map

Elefterios Soultanis

We use Almgren's framework of multi-valued maps to construct a multi-valued inverse $F : f (Ω) \to A_{d} (R^{n})$ of a quasiregular map $f : Ω \to R^{n}$ of finite degre…

math.MG2025

Spaces with Riemannian curvature bounds are universally infinitesimally Hilbertian

Jesús Núñez-Zimbrón, Enrico Pasqualetto, Elefterios Soultanis

We show that a metric space $X$ that, at every point, has a Gromov-Hausdorff tangent with the splitting property (i.e. every geodesic line splits off a factor $R$ ), is uni…

math.DG2025

Hilbert space factor of metric spaces

Thomas Foertsch, Alexander Lytchak, Elefterios Soultanis

We prove that any complete metric space has a unique decomposition as a direct product of a possibly finite or zero-dimensional Hilbert space and a space that does not split off li…

math.MG2024

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…

math.MG2024

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 $C$ of Banach (or metric) spaces: if…

math.CA2024

Fragment-wise differentiable structures

David Bate, Sylvester Eriksson-Bique, Elefterios Soultanis

The $p$ -modulus of curves, test plans, upper gradients, charts, differentials, approximations in energy and density of directions are all concepts associated to the theory of Sobol…

math.DG2023

Generalized products and Lorentzian length spaces

Elefterios Soultanis

We construct a Lorentzian length space with an orthogonal splitting on a product $I \times X$ of an interval and a metric space, and use this framework to consider the relationship…

math.DG2023

Asymptotically mean value harmonic functions in sub-Riemannian and RCD settings

Tomasz Adamowicz, Antoni Kijowski, Elefterios Soultanis

We consider weakly and strongly asymptotically mean value harmonic (amv-harmonic) functions on subriemannian and RCD settings. We demonstrate that, in non-collapsed RCD-spaces with…

math.MG2023★ 2 cited

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…

math.DG2022★ 4 cited

Filling minimality and Lipschitz-volume rigidity of convex bodies among integral current spaces

Giuliano Basso, Paul Creutz, Elefterios Soultanis

In this paper we consider metric fillings of convex bodies. We show that convex bodies $C \subset R^{n}$ are the unique minimal fillings of their boundary metrics among all i…

math.FA2022

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 $X \times Y$ can be determined from its factors.…

gr-qc2022

Causal bubbles in globally hyperbolic spacetimes

Leonardo García-Heveling, Elefterios Soultanis

We give an example of a spacetime with a continuous metric which is globally hyperbolic and exhibits causal bubbling. The metric moreover splits orthogonally into a timelike and a…

math.DG2022★ 1 cited

Tensorization of $p$ -weak differentiable structures

Sylvester Eriksson-Bique, Tapio Rajala, Elefterios Soultanis

We consider $p$ -weak differentiable structures that were recently introduced by the first and last named authors, and prove that the product of $p$ -weak charts is a $p$ -weak chart.…

math.MG2021★ 10 cited

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 $1 \leq p < \infty$ , by maximal directional derivatives along "generic" curves passing through a given point,…

math.DG2020

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…

math.MG2020

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…

math.AP2020

Asymptotically mean value harmonic functions in doubling metric measure spaces

Tomasz Adamowicz, Antoni Kijowski, Elefterios Soultanis

We consider functions with an asymptotic mean value property, known to characterize harmonicity in Riemannian manifolds, in doubling metric measure spaces. We show that the strongl…

math.MG2019

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…

math.MG2019

Metric currents and polylipschitz forms

Pekka Pankka, Elefterios Soultanis

We construct, for a locally compact metric space $X$ , a space of polylipschitz forms $Γ ˉ_{c}^{*} (X)$ , which is a pre-dual for the space of metric currents of $D_{*} (X)$ Ambr…

math.MG2018

Infinitesimal Hilbertianity of locally CAT( $κ$ )-spaces

Simone Di Marino, Nicola Gigli, Enrico Pasqualetto +1

We show that, given a metric space $(Y, d)$ of curvature bounded from above in the sense of Alexandrov, and a positive Radon measure $μ$ on $Y$ giving finite mass to bounded sets, t…

math.MG2018

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 $f : X \to Y$ between oriented cohomology manifolds $X$ and $Y$ induces a pull-back oper…

Infinitesimally Euclidean metric surfaces

Embeddability and rectifiability of Lipschitz differentiability spaces

Limits of mapping packages and tangents of Sobolev maps

Pull-back of differential forms by multi-valued Sobolev maps, and the quasiregularity of the multi-valued inverse of a quasiregular map

Spaces with Riemannian curvature bounds are universally infinitesimally Hilbertian

Hilbert space factor of metric spaces

Characterization of metric spaces with a metric fundamental class

Connections between metric differentiability and rectifiability

Fragment-wise differentiable structures

Generalized products and Lorentzian length spaces

Asymptotically mean value harmonic functions in sub-Riemannian and RCD settings

A non-compact convex hull in generalized non-positive curvature

Filling minimality and Lipschitz-volume rigidity of convex bodies among integral current spaces

Tensorization of quasi-Hilbertian Sobolev spaces

Causal bubbles in globally hyperbolic spacetimes

Tensorization of p-weak differentiable structures

Curvewise characterizations of minimal upper gradients and the construction of a Sobolev differential

Area minimizing surfaces in homotopy classes in metric spaces

Abstract and concrete tangent modules on Lipschitz differentiability spaces

Asymptotically mean value harmonic functions in doubling metric measure spaces

Maximal metric surfaces and the Sobolev-to-Lipschitz property

Metric currents and polylipschitz forms

Infinitesimal Hilbertianity of locally CAT(κ)-spaces

Pull-back of metric currents and homological boundedness of BLD-elliptic spaces

Tensorization of $p$ -weak differentiable structures

Infinitesimal Hilbertianity of locally CAT( $κ$ )-spaces