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

  • Weak regularity of the inverse under minimal assumptions (Joint with Stanislav Hencl and Aapo Kauranen). Preprint. [arxiv:1804.03449]
  • A Newman property for BLD-mappings Preprint. [arxiv:1709.08438]
  • Mappings of finite distortion: compactness of the branch set (Joint with Aapo Kauranen and Ville Tengvall). Preprint. [arxiv:1709.08724]
  • Stoilow's theorem revisited (Joint with Pekka Pankka.) Preprint. [arxiv:1701.05726]

Publications

  1. A Characterization Theorem for BLD-mappings between Metric Spaces The Journal of Geometric Analysis (2017) 27:2081 [arxiv:1509.01832]
  2. Note on local-to-global properties of BLD-mappings Proceedings of American Mathematical Society, 144 (2016), 599-607 [arxiv:1406.0320]
  3. Rigidity of extremal quasiregularly elliptic manifolds (Joint with Pekka Pankka.) Groups, Geometry and Dynamics 10 (2016), no. 2, 723-732 [arxiv:1307.7940]

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