Fokker-Planck Dynamics and Entropies for the Normalized Ricci Flow

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dc.creatorCarfora, Mauro
dc.date2005-07-15
dc.date2007-02-08
dc.date.accessioned2026-07-07T08:56:08Z
dc.date.available2026-07-07T08:56:08Z
dc.descriptionWe consider some elementary aspects of the geometry of the space of probability measures endowed with Wasserstein distance. In such a setting, we discuss the various terms entering Perelman's shrinker entropy, and characterize two new monotonic functionals for the volume-normalized Ricci flow. One is obtained by a rescaling of the curvature term in the shrinker entropy. The second is associated with a gradient flow obtained by adding a curvature-drift to Perelman's backward heat equation. We show that the resulting Fokker-Planck PDE is the natural diffusion flow for probability measures absolutely continuous with respect to the Ricci-evolved Riemannian measure, we discuss its exponential trend to equilibrium, and its relation with the viscous Hamilton-Jacobi equation.
dc.description48 pages, Latex;. This is the final version of the paper. References have been updated. This version contains an extended analysis of the relation between Fokker-Planck dynamics, along the backward Ricci flow, and the Wasserstein geometry on the space of probability measures
dc.identifierhttps://arxiv.org/abs/math/0507309
dc.identifierhttp://arxiv.org/abs/math/0507309
dc.identifierADVANCES IN THEORETICAL AND MATHEMATICAL PHYSICS. vol. 11, (2007) pp. 635-681
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/146503
dc.subjectDifferential Geometry
dc.subjectGeneral Relativity and Quantum Cosmology
dc.subjectMathematical Physics
dc.titleFokker-Planck Dynamics and Entropies for the Normalized Ricci Flow
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