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 by Bennett Chow, Peng Lu, Chow, Bennett +1
Mathematics · #53C25 #53C44 #Differential Geometry (math.DG) #FOS: Mathematics #math.DG #msc:53C25 #msc:53C44

paper · pdf · doi:10.48550/arxiv.math/0211194

28 pages, no figures

arxiv created 2002/11/12 · arxiv updated 2009/11/30

Abstract

The main result of this paper is: Given any constant C, there is (ε,k,L) such that if a complete, orientable, noncompact odd-dimensional manifold with bounded positive sectional curvature contains a (ε,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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