Fokker-Planck Dynamics and Entropies for the Normalized Ricci Flow
Carfora, Mauro
arXiv, 0507309 / Harvested from arXiv
Text on arXiv
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.
Publié le : 2005-07-15
Classification:  Mathematics - Differential Geometry,  General Relativity and Quantum Cosmology,  Mathematical Physics 
@article{0507309,
     author = {Carfora, Mauro},
     title = {Fokker-Planck Dynamics and Entropies for the Normalized Ricci Flow},
     journal = {arXiv},
     volume = {2005},
     number = {0},
     year = {2005},
     language = {en},
     url = {http://dml.mathdoc.fr/item/0507309}
}

Carfora, Mauro. Fokker-Planck Dynamics and Entropies for the Normalized Ricci Flow. arXiv, Tome 2005 (2005) no. 0, . http://gdmltest.u-ga.fr/item/0507309/