Acta mathematica scientia,Series B ›› 2024, Vol. 44 ›› Issue (5): 1639-1695.doi: 10.1007/s10473-024-0502-7

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HEAT KERNEL ON RICCI SHRINKERS (II)*

Yu Li1,2,†, Bing Wang1,2   

  1. 1. Institute of Geometry and Physics, University of Science and Technology of China, Hefei 230026, China;
    2. Hefei National Laboratory, Hefei 230088, China
  • Received:2023-02-07 Revised:2024-05-29 Online:2024-10-25 Published:2024-10-22
  • Contact: †Yu LI, E-mail,: yuli21@ustc.edu.cn
  • About author:Bing Wan, E-mail,: topspin@ustc.edu.cn
  • Supported by:
    Li's research was supported by the YSBR-001, the NSFC (12201597) and research funds from USTC (University of Science and Technology of China) and CAS (Chinese Academy of Sciences). Wang's research was supported by the YSBR-001, the NSFC (11971452, 12026251) and a research fund from USTC.

Abstract: This paper is the sequel to our study of heat kernel on Ricci shrinkers [29]. In this paper, we improve many estimates in [29] and extend the recent progress of Bamler [2]. In particular, we drop the compactness and curvature boundedness assumptions and show that the theory of $\mathbb{F}$-convergence holds naturally on any Ricci flows induced by Ricci shrinkers.

Key words: Ricci flow, Ricci shrinker, heat kernel

CLC Number: 

  • 53C44
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