A note on Perelman's LYH inequality

Abstract

We give a proof to the Li-Yau-Hamilton type inequality claimed by Perelman on the fundamental solution to the conjugate heat equation. The rest of the paper is devoted to improving the known differential inequalities of Li-Yau-Hamilton type via monotonicity formulae.

Cited by in corpus (3)

• Sharp logarithmic Sobolev inequalities on gradient solitons and applications
• Hamilton's gradient estimate for the heat kernel on complete manifolds
• Some gradient estimates for the heat equation on domains and for an equation by Perelman