KMS Of Academy of mathematics and systems sciences, CAS
| DIAMETER ESTIMATES FOR LONG-TIME SOLUTIONS OF THE KAHLER-RICCI FLOW | |
| Jian, Wangjian1; Song, Jian2 | |
| 2022-10-22 | |
| Source Publication | GEOMETRIC AND FUNCTIONAL ANALYSIS
 |
| ISSN | 1016-443X |
| Pages | 22 |
| Abstract | 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 |
| Indexed By | SCI |
| Language | 英语 |
| Funding Project | BICMR ; China Postdoctoral Science Foundation[2019M660827] ; National Natural Science Foundation of China[12288201] ; National Science Foundation[DMS-1711439] |
| WOS Research Area | Mathematics |
| WOS Subject | Mathematics |
| WOS ID | WOS:000871154100001 |
| Publisher | SPRINGER BASEL AG |
| Citation statistics | |
| Document Type | 期刊论文 |
| Identifier | http://ir.amss.ac.cn/handle/2S8OKBNM/60759 |
| Collection | 中国科学院数学与系统科学研究院 |
| Corresponding Author | Jian, Wangjian |
| Affiliation | 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 |
| Recommended Citation 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. |
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