Sharp upper diameter bounds for compact shrinking Ricci solitons

We give a sharp upper diameter bound for a compact shrinking Ricci soliton in terms of its scalar curvature integral and the Perelman’s entropy functional. The sharp cases could occur at round spheres. The proof mainly relies on a sharp logarithmic Sobolev inequality of gradient shrinking Ricci soli...

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Bibliographic Details
Published inAnnals of global analysis and geometry Vol. 60; no. 1; pp. 19 - 32
Main Author Wu, Jia-Yong
Format Journal Article
LanguageEnglish
Published Dordrecht Springer Netherlands 01.07.2021
Springer Nature B.V
Subjects
Analysis
Differential Geometry
Geometry
Global Analysis and Analysis on Manifolds
Mathematical Physics
Mathematics
Mathematics and Statistics
Solitary waves
Primary 53C20
Secondary 53C25
Shrinking Ricci soliton
Logarithmic Sobolev inequality
Diameter
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Summary:We give a sharp upper diameter bound for a compact shrinking Ricci soliton in terms of its scalar curvature integral and the Perelman’s entropy functional. The sharp cases could occur at round spheres. The proof mainly relies on a sharp logarithmic Sobolev inequality of gradient shrinking Ricci solitons and a Vitali-type covering argument.
ISSN:0232-704X
1572-9060
DOI:10.1007/s10455-021-09764-7