A No Shrinking Breather Theorem for Noncompact Harmonic Ricci Flows

Abstract

In this paper, we construct an ancient solution by using a given shrinking breather and prove a no shrinking breather theorem for noncompact harmonic Ricci flow under the condition that \({\rm{Sic}}: = {\rm{Ric}} - \alpha \nabla \phi \otimes \nabla \phi \) is bounded from below.