Hamilton differential Harnack inequality and W-entropy for Witten Laplacian on Riemannian manifolds

2017/07/06 by Songzi Li, Li, Songzi, Xiang‐Dong Li +1 · 1 citation
Mathematics · #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.1707.01644

openalex publication_date 2017/07/06 · openalex created_date 2017/07/14 · openalex updated_date 2026/07/28

Abstract

In this paper, we prove the Hamilton differential Harnack inequality for positive solutions to the heat equation of the Witten Laplacian on complete Riemannian manifolds with the CD(-K, m)-condition, where m∈ [n, ∞) and K≥ 0 are two constants. Moreover, we introduce the W-entropy and prove the W-entropy formula for the fundamental solution of the Witten Laplacian on complete Riemannian manifolds with the CD(-K, m)-condition and on compact manifolds equipped with (-K, m)-super Ricci flows.

Citations

• On the parabolic kernel of the Schrödinger operator

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• W-entropy formulas on super Ricci flows and Langevin deformation on Wasserstein space over Riemannian manifolds

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