Joint Seminar

Yuxin Ge and Lorenzo Mazzieri

16:15	Yuxin Ge (Toulouse)	Compactness of conformally compact Einstein manifolds in dimension 4 We show some compactness result of 4-dimensional conformally compact Einstein manifolds under the suitable assumptions on the topology of the manifolds, on the compactness of their conformal infinity and on some suitable conformal invariants. This is a joint work with Alice Chang and some improvements are obtained together with Jie Qing.
17:45	Lorenzo Mazzieri (Trento)	On the mass of static metrics with positive cosmological constant We introduce and discuss a notion of mass for static vacuum Einstein metrics with positive cosmological constant. In this context, we provide a positive mass statement as well as sharp area bounds for both cosmological horizons and horizons of black hole type. In the first case, these area bounds represent the natural extension of a well known result by Boucher, Gibbons and Horowitz, whereas for horizons of black hole type they can be seen as the analogue of the celebrated Riemannian Penrose Inequality. As an application, we deduce a uniqueness statement for the Schwarzschild--de Sitter static black hole. Time permitting, we show how the same circle of ideas applies to the analysis of Serrin's overdetermined boundary value problem for bounded domains with disconnected boundary (Joint work with S. Borghini and V. Agostiniani).

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