Kari Astala: Multifractal Rotational and stretching spectra for bilipschitz and quasiconformal mappings

Given a L-bilipschitz mapping of a planar domain, consider sets E where the mapping rotates with a chosen rate γ.

Question: How large can such sets be?

In this presentation we will determine the universal bounds (in terms of L) for the Hausdorff dimension of such sets.

Equally interesting are the universal multifractal bounds K-quasiconformal mappings; now one asks for the dimension of sets where the mapping rotates and stretches with given rates γ and α, respectively. Also here the universal bounds are determined.

The talk is based on a joint work with Tadeusz Iwaniec, Istvan Prause and Eero Saksman. The geometric approach above originates from our studies of vectorial calculus of variations. If time permits, also this connection will be discussed.