For Riemannian manifolds with a measure, we study the gradient estimates for positive smooth f-harmonic functions when the ∞-Bakry-Emery Ricci tensor and Ricci tensor are bounded from below, generalizing the classica...For Riemannian manifolds with a measure, we study the gradient estimates for positive smooth f-harmonic functions when the ∞-Bakry-Emery Ricci tensor and Ricci tensor are bounded from below, generalizing the classical ones of Yau （i.e., when ： is constant）.展开更多
In this paper, we investigate the positive solutions of ■u =■υ/■t on self-shrinkers, then get some gradient estimates and Harnack inequalities for the positive solutions.
文摘For Riemannian manifolds with a measure, we study the gradient estimates for positive smooth f-harmonic functions when the ∞-Bakry-Emery Ricci tensor and Ricci tensor are bounded from below, generalizing the classical ones of Yau （i.e., when ： is constant）.
基金Project supported by the National Natural Science Foundation of China(Grant No.11271343)the Natural Science Foundation of the Higher Education Institutions of Anhui(Grant No.KJ2018A0059)
文摘In this paper, we investigate the positive solutions of ■u =■υ/■t on self-shrinkers, then get some gradient estimates and Harnack inequalities for the positive solutions.
