On the asymptotic scalar curvature ratio of complete Type I-like ancient solutions to the Ricci flow on non-compact 3-manifolds

Details On the asymptotic scalar curvature ratio of complete Type I-like ancient solutions to the Ricci flow on non-compact 3-manifolds On the asymptotic scalar curvature ratio of complete Type I-like ancient solutions to the Ricci flow on non-compact 3-manifolds

2002-11-12

arxiv.org/abs/math/0211194v1

Mathematics

Differential Geometry

28 pages, no figures

Scientific paper

The main result of this paper is: Given any constant C, there is $(\epsilon,k,L)$ such that if a complete, orientable, noncompact odd-dimensional manifold with bounded positive sectional curvature contains a $(\epsilon,k,L)$-neck, then the asymptotic scalar curvature ratio is bigger or equal to C. As a application we proved that the asymptotic scalar curvature ratio of a complete noncompact ancient Type I-like solution to the Ricci flow with bounded positive sectional curvature on an orientable 3-manifold, is infinity.

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