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
7. 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.
6. Metric currents, polylipschitz forms and homological boundedness of BLD-elliptic spaces (2018). Pekka Pankka and Elefterios Soultanis. Sent for publication. Preprint available at https://arxiv.org/abs/1809.03009.
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.