SPEAKER: Ilmari Kangasniemi (Syracuse University)

TITLE: On the heterogeneous distortion inequality

ABSTRACT: In this talk, I discuss a joint work with Onninen, in which we study mappings f satisfying a version of the distortion inequality of K-quasiregular and K-quasiconformal maps with an extra additive term |f|^n σ^n, where σ is an L^n-integrable weight. We resolve a question of Astala, Iwaniec and Martin, who in the planar case n=2 showed a Liouville-type uniqueness theorem for mappings satisfying such a modified distortion inequality, and then asked whether this remains the case in higher dimensions. We also obtain sharp exponents of local Hölder continuity for such maps.