## Asian Journal of Mathematics

### Lower diameter bounds for compact shrinking Ricci solitons

#### 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.

#### Article information

Source
Asian J. Math., Volume 17, Number 1 (2013), 17-32.

Dates
First available in Project Euclid: 8 November 2013