On the Asymptotic Scalar Curvature Ratio of Complete Type I-like Ancient Solutions to the Ricci Flow on Noncompact 3-manifolds

Complete noncompact Riemannian manifolds with nonnegative sectional curvature arise naturally in the Ricci flow when one takes the limits of dilations about a singularity of a solution of the Ricci flow on a compact 3-manifold [H-95a]. To analyze the singularities in the Ricci flow one needs to understand these manifolds in depth. There are three invariants, asymptotic scalar curvature ratio, asymptotic volume ratio and aperture, that have been used to study the geometry of these manifolds at infinity.

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Published 1 January 2004