Geometry, Topology and Dynamics Seminar
Jeremy Tyson
Univ. of Illinois Urbana-Champaign
Frequency of Sobolev and quasiconformal dimension distortion
Abstract: The effect of Sobolev mappings on the dimensions of individual sets is well understood. I will discuss recent progress on quantitative bounds for the frequency of Hausdorff dimension increase for generic subspaces in the domain of a Sobolev mapping. We will consider two settings: the foliation of Euclidean space by parallel affine subspaces, and the Grassmannian manifold of all linear subspaces of a fixed dimension. In each case we quantify, at the level of Hausdorff measure on the parameterizing space, the size of the collection of such spaces whose dimension can be increased by a prespecified amount via a supercritical Sobolev mapping. Our results hold for maps into any target metric space, yet are new even for quasiconformal maps of planar domains. This talk is based on joint work with Zoltan Balogh, Roberto Monti and Pertti Mattila.
Monday April 7, 2014 at 3:00 PM in SEO 636