Rami Luisto



Research

My research interests are largely in the field of quasiconformal geometry, metric geometry and in regularity of Sobolev and BV mappings.

In the field of quasiconformal and metric geometry my spesific research questions are focused on branched covers, quasiregular mappings and mappings of finite distortion between Euclidean domains. In particular, I am interested in the so called branch set of a mapping, along with the interplay of the structure of the branch set and the local & global behaviour of the mapping. I'm also interested in the structure of BLD-mappings between (sub)Riemannian manifolds and more general path-metric spaces.

For Sobolev and BV mappings I am interested in finding optimal geometric bounds to guarantee analytic regularity conditions on the mappings.


To keep up with the current advances both in my field and the surrounding fields I use arxivist. I warmly recommend a daily dosage.

Preprints

  • A Newman property for BLD-mappings Preprint. [arxiv:1709.08438]
  • Characterization of branched covers with simplicial branch sets (Joint with Eden Prywes.) Preprint. [arxiv:1809.10874]
  • On proper branched coverings and a question of Vuorinen (Joint with Aapo Kauranen and Ville Tengvall). Preprint. [arxiv:1904.12645]

Publications

  1. Note on the compactness of the branch set of a branched cover (Joint with Aapo Kauranen and Ville Tengvall). Journal d'Analyse Mathematique (to appear). [arxiv:1709.08724]
  2. Stoilow's theorem revisited (Joint with Pekka Pankka.) Expositiones Mathematicae (to appear). [arxiv:1701.05726]
  3. Weak regularity of the inverse under minimal assumptions (Joint with Stanislav Hencl and Aapo Kauranen). Archive for Rational Mechanics and Analysis (to appear). [arxiv:1804.03449]
  4. Rigidity of extremal quasiregularly elliptic manifolds (Joint with Pekka Pankka.) Groups, Geometry and Dynamics 10 (2016), no. 2, 723-732 [arxiv:1307.7940]
  5. Note on local-to-global properties of BLD-mappings Proceedings of American Mathematical Society, 144 (2016), 599-607 [arxiv:1406.0320]
  6. A Characterization Theorem for BLD-mappings between Metric Spaces The Journal of Geometric Analysis (2017) 27:2081 [arxiv:1509.01832]

Theses

  • Interactions between quasiregular- and BLD-mappings Doctoral dissertation, University of Helsinki, 2016. PDF , e-thesis
  • BLD-kuvausten rajakäyttäytymisestä ja haarajoukoista (On the limit behaviour and branch sets of BLD-mappings) Licentiate thesis, (in finnish) University of Helsinki, 2014. PDF , e-thesis
  • On the non-existence of BLD-mappings between manifolds. Master's thesis, University of Helsinki, 2011. PDF , e-thesis
  • Kvasihyperbolinen metriikka (Quasihyperbolic metric) Bachelor's thesis, (in finnish) University of Helsinki, 2009. PDF