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Integral pinching characterization of compact shrinking Ricci solitons

Volume 173 / 2023

Yawei Chu, Rui Huang, Jundong Zhou Colloquium Mathematicum 173 (2023), 41-56 MSC: Primary 53C24; Secondary 53C20. DOI: 10.4064/cm8778-1-2023 Published online: 13 March 2023

Abstract

We investigate the pinching problem for shrinking compact Ricci solitons. Firstly, we show that every $n$-dimensional $(n\ge 4)$ shrinking compact Ricci soliton $(M^n,g)$ is isometric to a finite quotient of $\mathbb S^n$ under an $L^{n/2}$-pinching condition. Then we prove that the same result is still true for $(M^n,g)$ under an $L^p$-pinching condition for $p \gt 2/n$. The arguments rely mainly on algebraic curvature estimates and several important integral inequalities.

Authors

  • Yawei ChuSchool of Mathematics and Statistics
    Fuyang Normal University
    Fuyang, Anhui 236037
    People’s Republic of China
    e-mail
  • Rui HuangSchool of Mathematics and Statistics
    Fuyang Normal University
    Fuyang, Anhui 236037
    People’s Republic of China
    e-mail
  • Jundong ZhouSchool of Mathematics and Statistics
    Fuyang Normal University
    Fuyang, Anhui 236037
    People’s Republic of China
    e-mail

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