|
Sandra Huppert

Oberseminar Differentialgeometrie: Alix Deruelle (Sorbonne Université Paris ): A Lojasiewicz inequality for ALE Ricci flat metrics

Monday, 16.12.2019 16:15 im Raum SR4

Mathematik und Informatik

Abstract: This is a work in progress with Tristan Ozuch. We define a Perelman like functional for any Asymptotically Locally Euclidean metric. Such an energy has been introduced by Haslhofer in the setting of Asymptotially Flat metrics with non-negative scalar curvature. By computing its first variation, this functional is shown to be non-decreasing along the Ricci flow. Furthermore, it is constant in time if and only if the solution is ALE Ricci flat. Our main result is a Lojasiewicz inequality for this energy: this inequality will be crucial for at least two applications. On the one hand, ALE Ricci flat metrics are dynamically stable if and only if they locally maximize this functional. On the other hand, any small perturbation of an integrable and stable ALE Ricci flat metric with non-negative scalar curvature must be Ricci flat.



Angelegt am Friday, 06.09.2019 09:17 von Sandra Huppert
Geändert am Tuesday, 03.12.2019 11:37 von Gabi Dierkes
[Edit | Vorlage]

Oberseminare und sonstige Vorträge