Skip to content

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

Bennett Chow, Peng Lu

math.DGarXiv:math/0211194

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.

Create a lesson