4 papers
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…
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…
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…