Perelman-type no breather theorem for noncompact Ricci flows

Abstract

In this paper, we first show that a complete shrinking breather with Ricci curvature bounded from below must be a shrinking gradient Ricci soliton. This result has several applications. First, we can classify all complete $3$-dimensional shrinking breathers. Second, we can show that every complete shrinking Ricci soliton with Ricci curvature bounded from below must be gradient -- a generalization of Naber's result. Furthermore, we develop a general condition for the existence of the asymptotic shrinking gradient Ricci soliton, which hopefully will contribute to the study of ancient solutions.

28 pages

References in corpus (3)

• Compactness theory of the space of Super Ricci flows
• Entropy and heat kernel bounds on a Ricci flow background
• Structure theory of non-collapsed limits of Ricci flows

Cited by in corpus (2)

• Ancient Ricci flows with asymptotic solitons
• A no expanding breather theorem for noncompact Ricci flows