Séminaire de Géométrie

Mapping Solutions to the Constraint Equations

by Caterina Vâlcu (Ecole Polytechnique)

1180 (Bât E2)


Bât E2

Site Grandmont

We study initial data in General Relativity, which are defined as solutions to the constraint equations. The focus in this talk is a modified version of the conformal method proposed by David Maxwell. While the model seems more strongly justified from a geometrical standpoint, the resulting system becomes significantly more difficult to solve; it presents critical nonlinear terms, including gradient terms. We describe existence and stability while working in dimensions 3,4 and 5, under smallness assumptions and in the presence of a scalar field with positive potential. The tools we use are related to obtaining a priori estimates (compactness results) and a fixed-point theorem.