A no expanding breather theorem for noncompact Ricci flows

Abstract

In this note we show that, under certain curvature positivity conditions (the weak \({\text {PIC}}-2\) condition or the nonnegative bisectional curvature condition), a complete and noncompact expanding breather of the Ricci flow is also an expanding gradient Ricci soliton. This is the first no expanding breather theorem in the noncompact category.