Seminar
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Location: | SLMath: Eisenbud Auditorium |
Keywords and Mathematics Subject Classification (MSC)
Primary Mathematics Subject Classification
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Secondary Mathematics Subject Classification
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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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