Frederico Girão

The ADM mass of asymptotically flat hypersurfaces

We provide integral formulae for the ADM mass of asymptotically flat hypersurfaces in Riemannian manifolds with a certain warped product structure in a neighborhood of infinity, thus extending Lams recent results on Euclidean graphs to this broader context. As applications we exhibit, in any dimension, new classes of manifolds for which versions of the Positive Mass and Riemannian Penrose inequalities hold and discuss a notion of quasi-local mass in this setting. The proof explores a novel connection between the co-vector defining the ADM mass of a hypersurface as above and the Newton tensor associated to its shape operator, which takes place in the presence of an ambient Killing field.

Penrose inequalities and a positive mass theorem for charged black holes in higher dimensions

We use the inverse mean curvature flow to establish Penrose-type inequalities for time-symmetric Einstein-Maxwell initial data sets which can be suitably embedded as a hypersurface in Euclidean space

An Alexandrov–Fenchel-type inequality for hypersurfaces in the sphere

\mathbb R^{n+1}

An Alexandrov–Fenchel-Type Inequality in Hyperbolic Space with an Application to a Penrose Inequality

,

Positive mass and Penrose type inequalities for asymptotically hyperbolic hypersurfaces

n\geq 3

A rigidity result for the graph case of the Penrose inequality

. In particular, we prove a positive mass theorem for this class of charged black holes. As an application we show that the conjectured upper bound for the area in terms of the mass and the charge, which in dimension

A Penrose inequality for asymptotically locally hyperbolic graphs

n=3

The Gauss-Bonnet-Chern mass of higher codimension graphical manifolds

is relevant in connection with the Cosmic Censorship Conjecture, always holds under the natural assumption that the horizon is stable as a minimal hypersurface.

A spinorial approach to constant scalar curvature hypersurfaces in pseudo-hyperbolic manifolds

We find a monotone quantity along the inverse mean curvature flow and use it to prove an Alexandrov–Fenchel-type inequality for strictly convex hypersurfaces in the n-dimensional sphere,