Existence of solutions to the Lichnerowicz equation: A new proof

Romain Gicquaud (1)

1 FDP - Fédération de recherche Denis Poisson

We provide a complete study of the existence and uniqueness of solutions to the Lichnerowicz equation in general relativity with arbitrary mean curvature.

Mots clés: Einstein constraint equations; Non-constant mean curvature; Conformal method; Lichnerowicz equation; Compact manifold; Prescribed scalar curvature

Domaines: Relativité Générale et Cosmologie Quantique [gr-qc]; Physique mathématique [math-ph]

Romain Gicquaud. Existence of solutions to the Lichnerowicz equation: A new proof. Journal of Mathematical Physics, 2022, 63 (2), pp.022501. ⟨10.1063/5.0050920⟩. ⟨hal-02423741⟩