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.
Area minimizing surfaces in homotopy classes in metric spaces, with Stefan Wenger, 2021. [preprint]
Abstract and concrete tangent modules on Lipschitz differentiability spaces, with Toni Ikonen and Enrico Pasqualetto, 2020. [preprint]
Asymptotically mean value harmonic functions in metric measure spaces, with Tomasz Adamowicz and Antoni Kijowski, 2020. [preprint]
Path and quasihomotopy for Sobolev maps between manifolds, 2017. [preprint]
Infinitesimal hilbertianity of locally CAT(k)-spaces, Simone Di Marino, Nicola Gigli, Enrico Pasqualetto and Elefterios Soultanis, Journal of Geometric Analysis, published online, 2020.
Maximal metric discs and the Sobolev-to-Lipschitz property, Paul Creutz and Elefterios Soultanis, Calculus of Variations and Functional Analysis 59, Article number: 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 number: 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.