GRADIENT ESTIMATES FOR SOLUTIONS OF THE HEAT EQUATION UNDER RICCI FLOW

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	GRADIENT ESTIMATES FOR SOLUTIONS OF THE HEAT EQUATION UNDER RICCI FLOW
	Liu, Shiping
	2009-11-01
发表期刊	PACIFIC JOURNAL OF MATHEMATICS
ISSN	0030-8730
卷号	243 期号:1 页码:165-180
摘要	We establish first order gradient estimates for positive solutions of the heat equations on complete noncompact or closed Riemannian manifolds under Ricci flows. These estimates improve Guenther's results by weakening the curvature constraints. We also obtain a result for arbitrary solutions on closed manifolds under Ricci flows. As applications, we derive Harnack-type inequalities and second order gradient estimates for positive solutions of the heat equations under Ricci flow. The results in this paper can be considered as generalizing the estimates of Li-Yau and J. Y. Li to the Ricci flow setting.
关键词	gradient estimate Ricci flow heat equation Harnack inequality
语种	英语
WOS研究方向	Mathematics
WOS类目	Mathematics
WOS记录号	WOS:000272030500006
出版者	PACIFIC JOURNAL MATHEMATICS
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/7959
专题	中国科学院数学与系统科学研究院
通讯作者	Liu, Shiping
作者单位	Chinese Acad Sci, Acad Math & Syst Sci, Beijing 100190, Peoples R China
推荐引用方式 GB/T 7714	Liu, Shiping. GRADIENT ESTIMATES FOR SOLUTIONS OF THE HEAT EQUATION UNDER RICCI FLOW[J]. PACIFIC JOURNAL OF MATHEMATICS,2009,243(1):165-180.
APA	Liu, Shiping.(2009).GRADIENT ESTIMATES FOR SOLUTIONS OF THE HEAT EQUATION UNDER RICCI FLOW.PACIFIC JOURNAL OF MATHEMATICS,243(1),165-180.
MLA	Liu, Shiping."GRADIENT ESTIMATES FOR SOLUTIONS OF THE HEAT EQUATION UNDER RICCI FLOW".PACIFIC JOURNAL OF MATHEMATICS 243.1(2009):165-180.