# Research

#### My research interests

are nonsmooth. I am fascinated by connections between analytic concepts – such as Sobolev spaces, metric currents and second order calculus for spaces with lower Ricci curvature bounds (RCD spaces) – and topological and geometric ones, for example homology or cohomology groups, isoperimetric inequalities and so on. My current research emphasis roughly divides into

• homology and metric currents;
• existence and regularity of energy minima in homotopy classes of Sobolev maps;
• spaces with curvature bounds: Alexandrov and RCD-spaces; their analytic, geometric and topological properties, and also
• quasiregular and BLD-maps between nonsmooth metric spaces.

#### Articles and preprints

8. Pull-back of metric currents and homological boundedness of BLD-elliptic spaces (2019). Pekka Pankka and Elefterios Soultanis. Preprint available at https://arxiv.org/abs/1809.03009.

7. Metric currents and polylipschitz forms (2019). Pekka Pankka and Elefterios Soultanis. Preprint available at https://arxiv.org/abs/1809.03009.

6. Infinitesimal  hilbertianity of Alexandrov spaces with curvature bounded above (2018). Simone Di Marino, Nicola Gigli, Enrico Pasqualetto, Elefterios Soultanis. Preprint available at https://arxiv.org/abs/1812.02086.

5. Differential of metric valued Sobolev maps (2018), Nicola Gigli, Enrico Pasqualetto, Elefterios Soultanis. Sent for publication. Preprint available at https://arxiv.org/abs/1807.10063.

4. Path and quasihomotopy for Sobolev maps between manifolds (2017), Elefterios Soultanis. Sent for publication. Preprint available at https://arxiv.org/abs/1706.06043 .

3. Existence of \$p\$-energy minimizers in homotopy classes and lifts of Newtonian maps (2016),  Elefterios Soultanis. To appear in Journal d’Analyse Mathematique. Preprint available at http://arxiv.org/abs/1506.07767 .

2.  Homotopy classes of Newtonian spaces, Elefterios Soultanis, Rev. Mat. Iberoamecana 33 (2017), no. 3, 951 – 994.

1. Distortion of quasiconformal maps in terms of the quasihyperbolic metric, E. Soultanis ja M. Williams, J. Math. Anal. Appl. 402 (2013), no. 2, 626 – 634.