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Perelman's W-entropie for the Witten Laplacian and for the Fokker-Planck equation on Riemannian manifolds

GFM seminar

IIIUL, Auditorium

2011-05-13 15:30 .. 16:30

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by Xiangdong Li (Chinese Academy of Sciences)

In 2002, G. Perelman introduced the mysterious W-entropy for Ricci flow and proved its monotonicity along the conjugate heat equation. In this talk, we study the Perelman W-entropy for the heat equation of the Witten Laplacian and for the Fokker-Planck equation on complete Riemannian manifolds. Under some natural geometric condition in terms of dimension and the Bakry-Emery Ricci curvature, we prove the monotonicity and the rigidity theorems of the W-entropy for these equations.

Past conference highlights: Symmetries in Quantum Physics 2017; Advances in Mathematical Fluid Mechanics, Stochastic & Deterministic Methods; Quantum Integrable Systems and Geometry; Chern-Simons Gauge Theory: 20 years after; Second Workshop on Quantum Gravity and Noncommutative Geometry; Infinite Dimensional Algebras and Quantum Integrable Systems II; Stochastic Analysis in Mathematical Physics; Mathematics in Chemistry; Geometric Aspects of Integrable Systems; ICMP 2003