Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4668993 | Bulletin des Sciences Mathématiques | 2011 | 12 Pages |
Abstract
We establish a monotonicity theorem and a rigidity theorem for the Perelman W-entropy of the Fokker–Planck equation on complete Riemannian manifolds with non-negative m-dimensional Bakry–Emery Ricci curvature. Moreover, we give a probabilistic and kinetic interpretation of the W-entropy for the Fokker–Planck equation on complete Riemannian manifolds.
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