Séminaire OrléansRotational multifractal spectra for biLipschitz deformations
Kari Astala (Helsinki/Orléans)
Thursday 23 October 2014 14:00 - Orléans - Salle de Séminaire
Bi-Lipschitz mappings - perhaps the simplest geometric deformations - can have surprisingly delicate geometric properties. In this talk we ask how large can be a set $E$ where the map rotates or spirals with a given rate $\gamma$? We describe the optimal bounds for the size of such sets in terms of the Hausdorff dimension, and present the methods for proving these. The key points are a holomorphic deformation of bi-Lipschitz mappings and controlling this with a new kind of interpolation. The talk is based on joint work with Tadeusz Iwaniec, Istvan Prause and Eero Saksman.