The second variation of the Ricci expander entropy

Meng Zhu

Vol. 251 (2011), No. 2, 499–510

DOI: 10.2140/pjm.2011.251.499

Abstract

The critical points of the ℘ functional introduced by M. Feldman, T. Ilmanen and L. Ni are the expanding Ricci solitons, which are special solutions of the Ricci flow. On compact manifolds, expanding solitons coincide with Einstein metrics. In this paper, we compute the first and second variations of the entropy functional of the ℘ functional, and briefly discuss the linear stability of compact hyperbolic space forms.

Keywords

entropy functional, ν₊ functional, ℘ functional, linear stability, linear variation, negative Einstein manifold, second variation

Mathematical Subject Classification 2000

Primary: 53C21, 53C25, 53C44, 58J60

Milestones

Received: 30 January 2010

Accepted: 19 March 2010

Published: 3 June 2011