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.
Asymptotically mean value harmonic functions in metric measure spaces, with Tomasz Adamowicz and Antoni Kijowski, 2020. [preprint]
Maximal metric discs and the Sobolev-to-Lipschitz property, with Paul Creutz, 2019 (To appear in Calc. Var. and PDE). [preprint]
Infinitesimal hilbertianity of Alexandrov spaces with curvature bounded above, with Simone Di Marino, Nicola Gigli, and Enrico Pasqualetto, 2018. [preprint]
Path and quasihomotopy for Sobolev maps between manifolds, 2017. [preprint]
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.