My research interests
I work at the intersection of analysis and geometry in non-smooth settings, in particular on mappings with non-smooth domain and/or target (e.g. quasiregular and BLD-maps), and spaces with synthetic curvature bounds (e.g. Alexandrov and RCD spaces).
My background is in Sobolev type spaces over metric measure spaces, which I use along with metric currents and other tools from analysis on metric spaces to understand geometric and topological properties of the maps and spaces involved.
Recently I have focused on homological constraints on BLD-maps and Plateau-type problems on spaces with a quadratic isoperimetric inequality, both of which can be seen in the more general context of parametrization problems of non-smooth spaces. Energy minimization in homotopy classes of maps is a specific method to study maps and the information they transfer, but more generally I want to understand the connections (or lack of) between analysis, geometry and topology on the underlying spaces.
Filling minimality and Lipschitz-volume rigidity of convex bodies among integral current spaces, with Giuliano Basso and Paul Creutz, 2022. [preprint]
Tensorization of quasi-Hilbertian Sobolev spaces, with Sylvester Eriksson-Bique and Tapio Rajala, 2022. [preprint]
Tensorization of p-weak differentiable structures, with Sylvester Eriksson-Bique and Tapio Rajala, 2022. [preprint]
Asymptotically mean value harmonic functions in sub-Riemannian and RCD settings, Tomasz Adamowicz, Antoni Kijowski and Elefterios Soultanis, To Appear in Journal of Geometric Analysis, 2023.
Curvewise characterizations of minimal upper gradients and the construction of a Sobolev differential, Sylvester Eriksson-Bique and Elefterios Soultanis, To Appear in Analysis and PDE, 2023. [preprint]
Causal bubbles in globally hyperbolic spacetimes, Leonardo García-Heveling and Elefterios Soultanis, General Relativity and Gravitation 54, Article 155, 2022.
Asymptotically mean value harmonic functions in doubling metric measure spaces, Tomasz Adamowicz, Antoni Kijowski and Elefterios Soultanis, Geometry and Analysis in Metric Spaces 10(1), 344-372, 2022.
Area minimizing surfaces in homotopy classes in metric spaces, Elefterios Soultanis and Stefan Wenger, Transactions of the American Mathematical Society 375(7), 4711-4739, 2022.
Abstract and concrete tangent modules on Lipschitz differentiability spaces, Toni Ikonen, Enrico Pasqualetto and Elefterios Soultanis, Proceedings of the American Mathematical Society 150, 327-343, 2022.
Path and quasihomotopy for Sobolev maps between manifolds, Elefterios Soultanis, Journal of Functional Analysis 280(8), Article 108935, 2021.
Infinitesimal hilbertianity of locally CAT(k)-spaces, Simone Di Marino, Nicola Gigli, Enrico Pasqualetto and Elefterios Soultanis, Journal of Geometric Analysis 31, 7621 – 7685, 2021.
Maximal metric discs and the Sobolev-to-Lipschitz property, Paul Creutz and Elefterios Soultanis, Calculus of Variations and Partial Differential Equations 59, Article 177, 2020.
Pull-back of metric currents and homological boundedness of BLD-elliptic spaces, Pekka Pankka and Elefterios Soultanis, Analysis and Geometry in Metric Spaces 7(1), 212 – 249, 2019.
Metric currents and polylipschitz forms, Pekka Pankka and Elefterios Soultanis, Calculus of Variations and Partial Differential Equations 59, Article 76, 2020.
Differential of metric valued Sobolev maps, Nicola Gigli, Enrico Pasqualetto, Elefterios Soultanis, Journal of Functional Analysis 278(9), Article 108403, 2020.
Existence of p-energy minimizers in homotopy classes and lifts of Newtonian maps, Elefterios Soultanis, Journal d’Analyse Mathematique 137(2), 469 – 505, 2019.
Homotopy classes of Newtonian spaces, Elefterios Soultanis, Revista Matematica Iberoamecana 33(3), 951 – 994, 2017.
Distortion of quasiconformal maps in terms of the quasihyperbolic metric, Elefterios Soultanis and Marshall Williams, Journal of Mathematical Analysis and Applications 402(2), 626 – 634, 2013.