### 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

**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]

### Articles

**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.