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.