Mathematics – Differential Geometry
Scientific paper
2005-07-15
ADVANCES IN THEORETICAL AND MATHEMATICAL PHYSICS. vol. 11, (2007) pp. 635-681
Mathematics
Differential Geometry
48 pages, Latex;. This is the final version of the paper. References have been updated. This version contains an extended anal
Scientific paper
We 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.
No associations
LandOfFree
Fokker-Planck Dynamics and Entropies for the Normalized Ricci Flow does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Fokker-Planck Dynamics and Entropies for the Normalized Ricci Flow, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Fokker-Planck Dynamics and Entropies for the Normalized Ricci Flow will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-411669