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.

Preprints

Publications

  • Metric currents and polylipschitz forms. Pekka Pankka,  Elefterios Soultanis.  Calculus of Variations and Partial Differential Equations 59,  76 (2020). [ArXiv]
  • Differential of metric valued Sobolev mapsNicola Gigli, Enrico Pasqualetto, Elefterios Soultanis. Journal of Functional Analysis, vol. 278 (2020), no. 6, article 108403. [ArXiv]
  • Pull-back of metric currents and homological boundedness of BLD-elliptic spaces. Pekka Pankka,  Elefterios Soultanis.  Analysis and Geometry on Metric spaces 7   (2019), no. 1,  212-249. [ArXiv]
  • Existence of p-energy minimizers in homotopy classes and lifts of Newtonian maps.  Elefterios Soultanis, Journal d’Analyse Mathematique 137 (2019), no. 2, 469 – 505. [ArXiv]
  • Homotopy classes of Newtonian spaces. Elefterios Soultanis, Rev. Mat. Iberoamecana 33 (2017), no. 3, 951 – 994. [ArXiv]
  • Distortion of quasiconformal maps in terms of the quasihyperbolic metric. Elefterios Soultanis, Marshall Williams, J. Math. Anal. Appl. 402 (2013), no. 2, 626 – 634.