|COOKIES: By using this website you agree that we can place Google Analytics Cookies on your device for performance monitoring.|
Dynamical stability and instability of Ricci-flat metrics
If you have a question about this talk, please contact Neshan Wickramasekera.
Let M be a compact manifold. A Ricci-flat metric on M is a Riemannian metric with vanishing Ricci curvature. Ricci-flat metrics are fairly hard to construct, and their properties are of great interest. They are the critical points of the Einstein-Hilbert functional, the fixed points of Hamilton’s Ricci flow and the critical points of Perelman’s lambda-functional.
In this talk, we are concerned with the stability properties of Ricci-flat metrics under Ricci flow. We will prove the following stability and instability results. If a Ricci-flat metric is a local maximizer of lambda, then every Ricci flow starting close to it exists for all times and converges (modulo diffeomorphisms) to a nearby Ricci-flat metric. If a Ricci-flat metric is not a local maximizer of lambda, then there exists a nontrivial ancient Ricci flow emerging from it. This is joint work with Robert Haslhofer.
This talk is part of the Geometric Analysis and Partial Differential Equations seminar series.
This talk is included in these lists:
Note that ex-directory lists are not shown.
Other listsPhysics of Living Matter lectures Cambridge University Biological Society Chemical Engineering and Biotechnology
Other talksAsymptotic theory for acoustic instability of premixed combustion The arithmetic of hyperelliptic curves John Davey and Denise Dalbosco Dell'Aglio The Role of Embassies in European Climate Diplomacy Israeli Literature in a Post-National Age Use of the semi-geostrophic model in understanding large-scale atmosphere and ocean flows