Uniformly strong convergence of Kahler-Ricci flows on a Fano manifold  

作　　者：Feng Wang Xiaohua Zhu 

机构地区：[1]School of Mathematical Sciences,Zhejiang University,Hangzhou 310027,China [2]School of Mathematical Sciences,Peking University,Beijing 100871,China

出　　处：《Science China Mathematics》2022年第11期2337-2370,共34页中国科学：数学（英文版）

基　　金：supported by National Natural Science Foundation of China(Grant No.11971423);the Fundamental Research Funds for the Central Universities;supported by National Natural Science Foundation of China(Grant No.11771019);Beijing Science Foundation(Grant No.Z180004);National Key R&D Program of China(Grant No.SQ2020YFA070059).

摘　　要：In this paper,we study the uniformly strong convergence of the Kahler-Ricci flow on a Fano manifold with varied initial metrics and smoothly deformed complex structures.As an application,we prove the uniqueness of Kahler-Ricci solitons in the sense of diffeomorphism orbits.The result generalizes Tian-Zhu’s theorem for the uniqueness of of Kahler-Ricci solitons on a compact complex manifold,and it is also a generalization of Chen-Sun’s result of the uniqueness of Kahler-Einstein metric orbits.

关 键 词：Kahler-Ricci flow K¨ahler-Ricci solitons Q-Fano variety Gromov-Hausdorff topology 

分 类 号：O186.11[理学—数学]