DIAMETER ESTIMATES FOR LONG-TIME SOLUTIONS OF THE KAHLER-RICCI FLOW

doi:10.1007/s00039-022-00620-9

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	DIAMETER ESTIMATES FOR LONG-TIME SOLUTIONS OF THE KAHLER-RICCI FLOW
	Jian, Wangjian 1; Song, Jian 2
	2022-10-22
发表期刊	GEOMETRIC AND FUNCTIONAL ANALYSIS
ISSN	1016-443X
页码	22
摘要	It is well known that the Kahler-Ricci flow on a Kahler manifold X admits a long-time solution if and only if X is a minimal model, i.e., the canonical line bundle KX is nef. The abundance conjecture in algebraic geometry predicts that KX must be semi-ample when X is a projective minimal model. We prove that if KX is semi-ample, then the diameter is uniformly bounded for long-time solutions of the normalized Kahler-Ricci flow. Our diameter estimate combined with the scalar curvature estimate in Song and Tian (Am J Math 138(3):683-695, 2016) for long-time solutions of the Kahler-Ricci flow are natural extensions of Perelman's diameter and scalar curvature estimates for short-time solutions on Fano manifolds. As an application, the normalized Kahler-Ricci flow on a minimal threefold X always converges sequentially in Gromov-Hausdorff topology to a compact metric space homeomorphic to its canonical model X-can.
DOI	10.1007/s00039-022-00620-9
收录类别	SCI
语种	英语
资助项目	BICMR ; China Postdoctoral Science Foundation[2019M660827] ; National Natural Science Foundation of China[12288201] ; National Science Foundation[DMS-1711439]
WOS研究方向	Mathematics
WOS类目	Mathematics
WOS记录号	WOS:000871154100001
出版者	SPRINGER BASEL AG
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/60759
专题	中国科学院数学与系统科学研究院
通讯作者	Jian, Wangjian
作者单位	1.Chinese Acad Sci, Acad Math & Syst Sci, Inst Math, Beijing 100190, Peoples R China 2.Rutgers State Univ, Dept Math, Piscataway, NJ 08854 USA
推荐引用方式 GB/T 7714	Jian, Wangjian,Song, Jian. DIAMETER ESTIMATES FOR LONG-TIME SOLUTIONS OF THE KAHLER-RICCI FLOW[J]. GEOMETRIC AND FUNCTIONAL ANALYSIS,2022:22.
APA	Jian, Wangjian,&Song, Jian.(2022).DIAMETER ESTIMATES FOR LONG-TIME SOLUTIONS OF THE KAHLER-RICCI FLOW.GEOMETRIC AND FUNCTIONAL ANALYSIS,22.
MLA	Jian, Wangjian,et al."DIAMETER ESTIMATES FOR LONG-TIME SOLUTIONS OF THE KAHLER-RICCI FLOW".GEOMETRIC AND FUNCTIONAL ANALYSIS (2022):22.