Expanding solitons with non-negative curvature operator coming out of cones

Details Expanding solitons with non-negative curvature operator coming out of cones Expanding solitons with non-negative curvature operator coming out of cones

2010-08-08

arxiv.org/abs/1008.1408v1

Mathematics

Differential Geometry

16 pages

Scientific paper

We show that a Ricci flow of any complete Riemannian manifold without boundary with bounded non-negative curvature operator and non-zero asymptotic volume ratio exists for all time and has constant asymptotic volume ratio. We show that there is a limit solution, obtained by scaling down this solution at a fixed point in space, which is an expanding soliton coming out of the asymptotic cone at infinity.

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