Article Dans Une Revue Conformal Geometry and Dynamics of the American Mathematical Society Année : 2022

Scalar flat compactifications of Poincaré-Einstein manifolds and applications

Simon Raulot
  • Fonction : Auteur
  • PersonId : 847761

Résumé

We derive an integral inequality between the mean curvature and the scalar curvature of the boundary of any scalar flat conformal compactifications of Poincaré-Einstein manifolds. As a first consequence , we obtain a sharp lower bound for the first eigenvalue of the conformal half-Laplacian of the boundary of such manifolds. Secondly, a new upper bound for the renormalized volume is given in the four dimensional setting. Finally, some estimates on the first eigenvalues of Dirac operators are also deduced.
Fichier principal
Vignette du fichier
ScalarFlatMetric-PE.pdf (246.66 Ko) Télécharger le fichier
Origine Fichiers produits par l'(les) auteur(s)
Loading...

Dates et versions

hal-02290331 , version 1 (17-09-2019)

Identifiants

Citer

Simon Raulot. Scalar flat compactifications of Poincaré-Einstein manifolds and applications. Conformal Geometry and Dynamics of the American Mathematical Society, 2022, 26 (4), pp.46-66. ⟨10.1090/ecgd/371⟩. ⟨hal-02290331⟩
30 Consultations
101 Téléchargements

Altmetric

Partager

More