The Nonexistence of Noncompact Type-I Ancient 3-d $\kappa$-Solutions of Ricci Flow with Positive Curvature

Abstract

In this short paper, we show there do not exist three-dimensional noncompact $\kappa$-solutions of Ricci flow that have positive curvature and satisfy a Type-I bound. This represents progress towards the proof of Perelman's conjecture that the only complete noncompact three-dimensional $\kappa$-solution with positive curvature is the Bryant soliton.