Abstract
AbstractWe give an account on Otto’s geometrical heuristics for realizing, on a compact Riemannian manifold M, the L 2 Wasserstein distance restricted to smooth positive probability measures, as a Riemannian distance. The Hilbertian metric discovered by Otto is obtained as the base metric of a Riemannian submersion with total space, the group of diffeomorphisms of M equipped with the Arnol’d metric, and projection, the push-forward of a reference probability measure. The expression of the horizontal constant speed geodesics (time dependent optimal mass transportation maps) is derived using the Riemannian geometry of M as a guide.KeywordsRiemannian GeometryJacobian EquationOptimal TransportRiemannian SubmersionRiemannian FoliationThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
