Séminaire de GéométriePenrose type inequalities for asymptotically hyperbolic graphs
Anna Sakovich (Steckholm)
jeudi 10 mai 2012 14:00 - Tours - Salle 2290 (Bât E2)
Penrose type inequalities is a collective term used to describe a class of inequalities giving a lower bound for the mass of an initial data set (M,g,K) (here (M,g) is a Riemannian manifold, K is a symmetric 2-tensor) with nonnegative energy density in terms of the area of suitable hypersurfaces representing black holes. This topic has remained an active area of research since 1973, when an inequality of this kind was first proposed by Penrose. If (M,g) is asymptotically Euclidean then taking K=0 (time symmetric case) one can formulate what is know as the Riemannian Penrose inequality, first proved in 2001 (Huisken&Ilmanen, Bray). A simplified proof of this result was obtained by Lam in 2010 for asymptotically Euclidean manifolds which are the graphs of a smooth function over R^n. After reviewing these results, we will consider time symmetric asymptotically hyperbolic initial data sets. Almost no results being available in this direction, we will present a proof of Penrose type inequalities for asymptotically hyperbolic manifolds which are the graphs of a smooth asymptotically constant function over H^n. This result is inspired by the aforementioned work of Lam, and is a joint work of Dahl, Gicquaud, and the speaker.