Expanding solitons with non-negative curvature operator coming out of cones
By F. Schulze, Miles Simon. 2010
74 citations recorded by the source corpus.
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.
Subfields: Applied Mathematics, Geometry and Topology
View Paper: https://www.semanticscholar.org/paper/2a2e2ad29406c6670072fd9429be35032c227b59
How researchers see this paper
The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.
In Applied Mathematics
- Esther Cabezas-Rivas
- Burkhard Wilking
- W. Ziller
- W. Wylie
- Peter Petersen
- Frederick Wilhelm
- Huaihuo Cao
- S. Brendle
In Geometry and Topology
- Esther Cabezas-Rivas
- Burkhard Wilking
- W. Ziller
- W. Wylie
- Peter Petersen
- Marco Radeschi
- Frederick Wilhelm
- Huaihuo Cao
Citations in the corpus
- How to produce a Ricci Flow via Cheeger-Gromoll exhaustion (2011, methodology): “For immortal solutions we will also give an analysis of the long time behavior of the flow: In the case of an initial metric with Euclidean volume growth we remark that a result of Simon and Schulze [42] can be adjusted to see that a suitably rescaled Ricci flow subconverges to an expanding soliton ”