Diff. Geom, Math. Phys., PDE Seminar: Nassif Ghoussoub
- Date: 09/24/2013
- Time: 15:30
University of British Columbia
Symmetric Monge-Kantorovich problems and polar decompositions of vector fields
For any given integer N larger than 2, we show that every bounded measurable vector field is N-cyclically monotone up to a measure preserving N-involution. The proof involves the solution of a multidimensional symmetric Monge-Kantorovich problem, which we first study in the case of a general cost function on a product domain. The proof exploits a remarkable duality between measure preserving transformations that are N-involutions and those Hamiltonians that are N-cyclically antisymmetric.
Location: ESB 2012