On the asymptotic scalar curvature ratio of complete Type I-like ancient solutions to the Ricci flow on noncompact 3-manifolds
نویسندگان
چکیده
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. Let (Mn, g) be a complete noncompact Riemannian manifold with nonnegative sectional curvature and let O ∈ M be some point which we call the origin. The asymptotic scalar curvature ratio (ASCR) is defined by
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