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

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