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Home » OT Programmatic Seminar: Symmetric Monge-Kantorovich problems and polar decompositions of vector fields

Seminar

OT Programmatic Seminar: Symmetric Monge-Kantorovich problems and polar decompositions of vector fields October 08, 2013 (03:45PM PDT - 04:45PM PDT)
Parent Program: Optimal Transport: Geometry and Dynamics
Location: MSRI: Simons Auditorium
Speaker(s) Nassif Ghoussoub (University of British Columbia)
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For any given integer N larger than 2, we show that every bounded measurable vector field on a bounded domain in Euclidean space 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. The proof exploits a remarkable duality between measure preserving transformations that are N-involutions and Hamiltonian functions that are N-cyclically antisymmetric.

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