37 citations · 144 across the 21 of their papers we have counts for
23 papers
On the topology of the space of vacuum initial data sets
Romain Gicquaud, Jonathan Glöckle
We show that the space of vacuum initial data sets on a closed manifold often has many non-trivial homotopy groups. The starting point is a result of the second named author, which…
A new approach towards the construction of initial data in general relativity with positive Yamabe invariant and arbitrary mean curvature
Armand Coudray, Romain Gicquaud
This paper revisits the classical construction of initial data using the conformal method, as originally proposed by Holst, Nagy, and Tsogtgerel and later refined by Maxwell. We de…
A note on Poincaré-Sobolev type inequalities on compact manifolds
Romain Gicquaud
We prove a Poincaré-Sobolev type inequality on compact Riemannian manifolds where the deviation of a function from a biased average, defined using a density, is controlled by the u…
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…
What Uniqueness for the Holst-Nagy-Tsogtgerel--Maxwell Solutions to the Einstein Conformal Constraint Equations?
Romain Gicquaud
This paper addresses the issue of uniqueness of solutions in the conformal method for solving the constraint equations in general relativity with arbitrary mean curvature as develo…
Existence of solutions to the Lichnerowicz equation: a new proof
Romain Gicquaud
We provide a complete study of existence and uniqueness of solutions to the Lichnerowicz equation in general relativity with arbitrary mean curvature.
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…
Solutions to the Einstein constraint equations with a small TT-tensor and vanishing Yamabe invariant
Romain Gicquaud
In this note we prove an existence result for the Einstein conformal constraint equations for metrics with vanishing Yamabe invariant assuming that the TT-tensor is small in .
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…
Bifurcating solutions of the Lichnerowicz equation
Piotr Chruściel, Romain Gicquaud
We give an exhaustive description of bifurcations and of the number of solutions of the vacuum Lichnerowicz equation with positive cosmological constant on with $U(…
Solutions to the Einstein-scalar field constraint equations with a small TT-tensor
Romain Gicquaud, The Cang Nguyen
In this paper, we prove a far-from-CMC result similar to the ones obtained by Holst, Nagy, Tsogtgerel and Maxwell for the conformal Einstein-scalar field constraint equations on co…
Limit equation for vacuum Einstein constraints with a translational Killing vector field in the compact hyperbolic case
Romain Gicquaud, Cecile Huneau
We construct solutions to the constraint equations in general relativity using the limit equation criterion introduced by Dahl, Humbert and the first author. We focus on solutions…
A new point of view on the solutions to the Einstein constraint equations with arbitrary mean curvature and small TT-tensor
Romain Gicquaud, Quôc Anh Ngô
In this short note, we give a construction of solutions to the Einstein constraint equations using the well known conformal method. Our method gives a result similar to the one in…
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…
A non-existence result for a generalization of the equations of the conformal method in general relativity
Mattias Dahl, Romain Gicquaud, Emmanuel Humbert
The constraint equations of general relativity can in many cases be solved by the conformal method. We show that a slight modification of the equations of the conformal method admi…
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…
A limit equation associated to the solvability of the vacuum Einstein constraint equations using the conformal method
Mattias Dahl, Romain Gicquaud, Emmanuel Humbert
Let be a compact Riemannian manifold on which a trace-free and divergence-free and a positive function , , are fixed. In this paper, we…
A large class of non constant mean curvature solutions of the Einstein constraint equations on an asymptotically hyperbolic manifold
Romain Gicquaud, Anna Sakovich
We construct solutions of the constraint equation with non constant mean curvature on an asymptotically hyperbolic manifold by the conformal method. Our approach consists in decrea…
Linearization stability of the Einstein constraint equations on an asymptotically hyperbolic manifold
Romain Gicquaud
We study the linearization stability of the Einstein constraint equations on an asymptotically hyperbolic manifold. In particular we prove that these equations are linearization st…
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…