Hamilton's gradient estimates and a monotonicity formula for heat flows on metric measure spaces. (January 2016)

• Record Type: Journal Article
• Authors: Jiang, Renjin; Zhang, Huichun
• Is Part Of: Nonlinear analysis. Volume 131(2016)
• Page Start: 32
• Page End: 47
• Publication Date: 2016-01
• Subjects: 53C23 -- 35K05; Metric measure space -- Curvature-dimension condition -- Hamilton's gradient estimates; Mathematical analysis -- Periodicals; Functional analysis -- Periodicals; Nonlinear theories -- Periodicals; Analyse mathématique -- Périodiques; Analyse fonctionnelle -- Périodiques; Théories non linéaires -- Périodiques; Functional analysis; Mathematical analysis; Nonlinear theories; Periodicals; Electronic journals; 515.7248
• DOI: 10.1016/j.na.2015.08.011
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: In this paper, we extend the Hamilton's gradient estimates (Hamilton 1993) and a monotonicity formula of entropy (Ni 2004) for heat flows from smooth Riemannian manifolds to (non-smooth) metric measure spaces with appropriate Riemannian curvature-dimension condition.