A measure and orientation preserving homeomorphism of a cube with Jacobian equal to -1 almost everywhere.

Analysis, Geometry & Topology
Tuesday, October 3, 2017 - 15:00 to 15:50
Thackeray 427

Abstract or Additional Information

 

I will show how to construct an almost everywhere approximately differentiable, orientation and measure preserving homeomorphism of a unit n-dimensional cube onto itself, whose Jacobian is equal to -1 a.e. Moreover I will prove that the homeomorphism can be uniformly approximated by orientation and measure preserving diffeomorphisms. The talk is based on my joint work with Pawel Goldstein.