On Ricci flow invariant curvature cones
Event details
| Date | 18.02.2014 |
| Hour | 16:15 › 17:15 |
| Speaker | Thomas Richard (EPFL) |
| Location |
MA A3 31
|
| Category | Conferences - Seminars |
Geometry and Dynamics Seminar
Abstract: This is a joint work with H. Seshadri (IISc Bangalore).
The Ricci flow is a parabolic evolution equation for Riemannian metrics which has found important geometric applications (namely the proof of the Poincaré conjecture and of the differentiable sphere theorem). In these applications, it is useful to find conditions on the curvature which are preserved by the Ricci flow. These conditions are encoded by convex cones in a space of tensors which have the same symmetries as the Riemann curvature tensor. A suitable maximum principle for parabolic systems shows that the preservation of these conditions is equivalent to the stability of the associated cone under the flow of an explicit quadratic vector field. We show some generals result on such cones, which show some kind of strong dichotomy between the condition `nonnegative scalar curvature' and stronger ones.
Abstract: This is a joint work with H. Seshadri (IISc Bangalore).
The Ricci flow is a parabolic evolution equation for Riemannian metrics which has found important geometric applications (namely the proof of the Poincaré conjecture and of the differentiable sphere theorem). In these applications, it is useful to find conditions on the curvature which are preserved by the Ricci flow. These conditions are encoded by convex cones in a space of tensors which have the same symmetries as the Riemann curvature tensor. A suitable maximum principle for parabolic systems shows that the preservation of these conditions is equivalent to the stability of the associated cone under the flow of an explicit quadratic vector field. We show some generals result on such cones, which show some kind of strong dichotomy between the condition `nonnegative scalar curvature' and stronger ones.
Practical information
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Organizer
- Martins Bruveris, Sonja Hohloch, Marc Troyanov