Open Access
December 2009 A nonholonomic Moser theorem and optimal transport
Boris Khesin, Paul Lee
J. Symplectic Geom. 7(4): 381-414 (December 2009).


We prove the following nonholonomic version of the classical Moser theorem: given a bracket-generating distribution on a connected compact manifold (possibly with boundary), two volume forms of equal total volume can be isotoped by the flow of a vector field tangent to this distribution. We describe formal solutions of the corresponding nonholonomic mass transport problem and present the Hamiltonian framework for both the Otto calculus and its nonholonomic counterpart as infinite-dimensional Hamiltonian reductions on diffeomorphism groups.

Finally, we define a nonholonomic analog of the Wasserstein (or, Kantorovich) metric on the space of densities and prove that the subriemannian heat equation defines a gradient flow on the nonholonomic Wasserstein space with the potential given by the Boltzmann relative entropy functional.


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Boris Khesin. Paul Lee. "A nonholonomic Moser theorem and optimal transport." J. Symplectic Geom. 7 (4) 381 - 414, December 2009.


Published: December 2009
First available in Project Euclid: 22 October 2009

zbMATH: 1247.58005
MathSciNet: MR2551999

Rights: Copyright © 2009 International Press of Boston

Vol.7 • No. 4 • December 2009
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