Diff. Geom, Math. Phys., PDE Seminar: Nassif Ghoussoub

  • Date: 09/24/2013
  • Time: 15:30
Nassif Ghoussoub, UBC

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.

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Location: ESB 2012