A note on convergence of noncompact nonsingular solutions of the Ricci flow

Abstract

We extend some convergence results on nonsingular compact Ricci flows in the papers by Hamilton [Comm. Anal. Geom. 7 (1999), pp. 695–729], Sesum [Math. Res. Lett. 12 (2005), pp. 623–632] and Fang, Zhang, and Zhang [J. Geom. Anal. 20 (2010), pp. 592–608] to certain infinite volume noncompact cases which are “partially” nonsingular. As an application, for a finite time singularity which is partially type I, it is shown that a blow up limit is a gradient shrinking soliton.