37 citations · 144 across the 21 of their papers we have counts for
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A definition of the mass aspect function for weakly regular asymptotically hyperbolic manifolds
Romain Gicquaud, Anna Sakovich
In contrast to the well-known and unambiguous notion of ADM mass for asymptotically Euclidean manifolds, the notion of mass for asymptotically hyperbolic manifolds admits several i…
Prescribed non positive scalar curvature on asymptotically hyperbolic manifolds with application to the Lichnerowicz equation
Romain Gicquaud
We study the prescribed scalar curvature problem, namely finding which function can be obtained as the scalar curvature of a metric in a given conformal class. We deal with the cas…
Mass-like invariants for asymptotically hyperbolic metrics. Part I: Classification
Julien Cortier, Mattias Dahl, Romain Gicquaud
In this article, we classify the set of asymptotic mass-like invariants for asymptotically hyperbolic metrics. It turns out that the standard mass is just one example among the two…
On the asymptotic behavior of Einstein manifolds with an integral bound on the Weyl curvature
Romain Gicquaud, Dandan Ji, Yuguang Shi
In this paper we consider the geometric behavior near infinity of some Einstein manifolds with Weyl curvature belonging to a certain space. Namely, we show that if…
Asymptotically hyperbolic manifolds with small mass
Mattias Dahl, Romain Gicquaud, Anna Sakovich
For asymptotically hyperbolic manifolds of dimension with scalar curvature at least equal to the conjectured positive mass theorem states that the mass is non-negativ…
Penrose type inequalities for asymptotically hyperbolic graphs
Mattias Dahl, Romain Gicquaud, Anna Sakovich
In this paper we study asymptotically hyperbolic manifolds given as graphs of asymptotically constant functions over hyperbolic space $\bH^n$. The graphs are considered as subsets…
Conformal compactification of asymptotically locally hyperbolic metrics II: Weakly ALH metrics
Romain Gicquaud
In this paper we pursue the work initiated in \cite{Bahuaud, BahuaudGicquaud}: study the extent to which conformally compact asymptotically hyperbolic metrics can be characterized…
Conformal compactification of asymptotically locally hyperbolic metrics
Eric Bahuaud, Romain Gicquaud
In this paper we study the extent to which conformally compact asymptotically hyperbolic metrics may be characterized intrinsically. Building on the work of the first author, we pr…
De l'équation de prescription de courbure scalaire aux équations de contrainte en relativité générale sur une variété asymptotiquement hyperbolique
Romain Gicquaud
Two problems concerning asymptotically hyperbolic manifolds with an inner boundary are studied. First, we study scalar curvature presciption with either Dirichlet or mean curvature…