2017/07/06 by Songzi Li, Xiang-Dong Li, Li, Songzi +2 · 2 citations
Mathematics · #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Nonlinear Partial Differential Equations #math.DG
paper · pdf · doi:10.48550/arxiv.1707.01644
To appear in Journal of Functional Analysis. This paper is an improved version of a part of our previous preprint [14] (arxiv:1412.7034, version1 (22 December 2014) and version 2 (7 February 2016))
openalex publication_date 2017/07/06 · openalex created_date 2017/07/14 · arxiv created 2017/10/10 · arxiv updated 2017/10/11 · openalex updated_date 2026/07/28
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.