Asian Journal of Mathematics

Volume 17 (2013)

Number 1

Lower diameter bounds for compact shrinking ricci solitons

Pages: 17 – 32



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

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


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.


shrinking Ricci soliton, diameter bound

2010 Mathematics Subject Classification

Primary 53C21. Secondary 53C20.

Published 21 March 2013