### 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.

### Preprints

**Causal bubbles in globally hyperbolic spacetimes, **with Leonardo García-Heveling, 2022. [preprint]

**Tensorization of p-weak differentiable structures,** with Sylvester Eriksson-Bique and Tapio Rajala, 2022. [preprint]

**Curvewise characterizations of minimal upper gradients and the construction of a Sobolev differential, **with Sylvester Eriksson-Bique, 2021. [preprint]

**Asymptotically mean value harmonic functions in metric measure spaces**, with Tomasz Adamowicz and Antoni Kijowski, 2020. [preprint]

### Publications

**Area minimizing surfaces in homotopy classes in metric spaces, **Elefterios Soultanis and Stefan Wenger, *Transactions of the American Mathematical Society *375, no. 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 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.