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

文献类型：期刊论文

作者Jian, Wangjian1; Song, Jian2
刊名GEOMETRIC AND FUNCTIONAL ANALYSIS
出版日期2022-10-22
页码22
ISSN号1016-443X
DOI10.1007/s00039-022-00620-9
英文摘要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.
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
语种英语
WOS记录号WOS:000871154100001
出版者SPRINGER BASEL AG
源URL[http://ir.amss.ac.cn/handle/2S8OKBNM/60758]  
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.

入库方式： OAI收割

来源：数学与系统科学研究院

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