Generalized dimension distortion under planar Sobolev mappings
Abstract: It is well-known that a planar quasiconformal mapping
preserves the class of sets of Hausdorff dimension strictly less than two.
In fact, Astala's theorem gives essentially sharp estimates for the dimension
distortion. A mapping of exponentially integrable distortion can map a set,
say, of dimension one to a set of dimension two. However, estimates for the
dimension distortion can be proved in refined scales. As a tool, we describe
the setting for general (continuous) Sobolev mappings.
University of Jyvaskyla