37 citations · 144 across the 21 of their papers we have counts for
11 papers · 1 filter
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…
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.
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(…
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…
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…
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…