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京东 11.11 红包
Timothy Buttsworth：The Einstein-Hilbert functional along Ebin geodesics
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https://www.youtube.com/watch?v=NPr00-OA5bY Australian Geometric PDE Seminar Season 03 - Graduate and Early Career Research Seminar Homepage：https://oz-geom-pde.github.io/season03/ The Einstein-Hilbert functional along Ebin geodesics. Speaker: Timothy Buttsworth (University of Queensland) Date: 26 August 2022 Abstract：Given a closed manifold M, the set S of Riemannian metrics with prescribed volume form V is totally geodesic with respect to the Ebin metric; by a classical result of Moser, S contains all possible Riemannian structures on M. In this talk, I will describe some classical results on the behaviour of the Einstein-Hilbert functional on S, and how these results have been used to construct new Einstein metrics. I will also describe a new result that applies when M is at least five-dimensional: given a Riemannian metric g in S, there is an open and dense set of Ebin geodesics on S starting at g (in the smooth Whitney topology), along which scalar curvature converges to - infinity uniformly on M. This is joint work with Christoph Bohm and Brian Clark. Christoph Böhm , Timothy Buttsworth and Brian Clarke——“Scalar curvature along Ebin geodesics”：https://doi.org/10.1515/crelle-2024-0033 Let M be a smooth, compact manifold and let Nμ denote the set of Riemannian metrics on M with smooth volume density μ. For a given g0∈Nμ, we show that if dim(M)≥5, then there exists an open and dense subset Yg0⊂Tg0Nμ (in the C∞ topology) so that for each h∈Yg0, the (Nμ,L2) Ebin geodesic γh(t) with γh(0)=g0 and γ′h(0)=h satisfies limt→∞ R(γh(t))=−∞, uniformly.
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