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

Abstract

We consider Ricci flow of complete Riemannian manifolds which have bounded non-negative curvature operator, non-zero asymptotic volume ratio and no boundary. We prove scale invariant estimates for these solutions. Using these estimates, we show that there is a limit solution, obtained by scaling down this solution at a fixed point in space. This limit solution is an expanding soliton coming out of the asymptotic cone at infinity.

v.2. Added some missing references and made some minor rearrangements.14 pages

References in corpus (4)

• Recent Progress on Ricci Solitons
• Ricci flow of non-collapsed 3-manifolds whose Ricci curvature is bounded from below
• On the simply connectedness of non-negatively curved Kähler manifolds and applications
• Ricci expanders and type III Ricci flow