Asian Journal of Mathematics

Lower diameter bounds for compact shrinking Ricci solitons

Akito Futaki and Yuji Sano

Full-text: Open access

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

Permanent link to this document
https://projecteuclid.org/euclid.ajm/1383923434

Mathematical Reviews number (MathSciNet)
MR3038723

Zentralblatt MATH identifier
1281.53046

Subjects
Primary: 53C21: Methods of Riemannian geometry, including PDE methods; curvature restrictions [See also 58J60]
Secondary: 53C20: Global Riemannian geometry, including pinching [See also 31C12, 58B20]

Keywords
Shrinking Ricci soliton diameter bound

Citation

Futaki, Akito; Sano, Yuji. Lower diameter bounds for compact shrinking Ricci solitons. Asian J. Math. 17 (2013), no. 1, 17--32. https://projecteuclid.org/euclid.ajm/1383923434


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