|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 listsFuture of Sustainable Development in South Asia Forum for Youth Participation and Democracy Cambridge-Africa Programme
Other talksAlterations of brain function in pre-dementia Alzheimer’s disease: implications for early diagnosis ONE DAY MEETING - Biomimetics Plenary Lecture 11: The evolution of groups and microbial collectives Latent variable models: factor analysis and all that Fault-Tolerant Predictive Control: A Gaussian Process Model Based Approach “Nanomedicines for HIV”