I got my PhD in University of Jyväskylä in 2015 under supervision of Pekka Koskela. During 2016-2017 I spent 1,5 years in Charles University in Prague as a postdoc working with Stanislav Hencl.
I am interested in areas of analysis which are in some way related to complex analysis and conformal mappings. That is, topics such as quasiconformal and quasiregular mappings and Sobolev homeomorphisms. Lately, I have been involved most with the latter. I am also interested and trying to expand my knowledge in areas close to these topics such as calculus of variations, geometric measure theory and partial differential equations.
A. Kauranen and P. Koskela, “Boundary blow-up under Sobolev map-
pings,” Anal. PDE 7 (2014), no. 8, 1839–1850.
R. Jiang and A. Kauranen, ”Korn’s inequality and John domains,” Calc. Var. Partial Differential Equations 56 (2017), no. 4,
S. Hencl and A. Kauranen, ”Sobolev homeomorphisms in W 1,k and the Lusin’s condition (N) on k-
dimensional subspaces,” Ann. Acad. Sci. Fenn., to appear
A. Kauranen, "Generalized dimension estimates for images of porous sets in metric spaces," Ann. Acad. Sci. Fenn. Math. 41 (2016), no. 1, 85–102