Paris/Berkeley/Bonn/Zürich Analysis Seminar: Morse-Sard type results for Sobolev mappings

Seminar | January 26 | 9:10-10 a.m. | 238 Sutardja Dai Hall

 Jan Kristensen, Oxford University

 Department of Mathematics

The Morse-Sard theorem, and the generalizations by Dubovitskii and Federer, have numerous applications and belong to the core results of multivariate calculus for smooth mappings. In this talk we discuss extensions of these results to suitable classes of Sobolev mappings. The quest for optimal versions of the results leads one to consider possibly nondifferentiable mappings that in turn warrants new interpretations. A key point of the proofs is to show that the considered Sobolev mappings enjoy Luzin N type properties with respect to lower dimensional Hausdorff contents. The talk is based on joint work with Jean Bourgain, Piotr Hajlasz and Mikhail Korobkov.