Asian Journal of Mathematics

Volume 17 (2013)

Number 1

Lower diameter bounds for compact shrinking ricci solitons

Pages: 17 – 32

DOI: http://dx.doi.org/10.4310/AJM.2013.v17.n1.a2

Authors

Akito Futaki (Graduate School of Mathematical Sciences, University of Tokyo, Japan)

Yuji Sano (Graduate School of Science and Technology, Kumamoto University, Japan)

Abstract

It is shown that the diameter of a compact shrinking Ricci soliton has a universal lower bound. This is proved by extending universal estimates for the first non-zero eigenvalue of Laplacian on compact Riemannian manifolds with lower Ricci curvature bound to a twisted Laplacian on compact shrinking Ricci solitons.

Keywords

shrinking Ricci soliton, diameter bound

2010 Mathematics Subject Classification

Primary 53C21. Secondary 53C20.

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