Positive mass theorem for the Paneitz-Branson operator

Emmanuel Humbert (1) , Simon Raulot (2)

1 IECN - Institut Élie Cartan de Nancy
2 UNINE - Institut de Mathématiques

We prove that under suitable assumptions, the constant term in the Green function of the Paneitz-Branson operator on a compact Riemannian manifold $(M,g)$ is positive unless $(M,g)$ is conformally diffeomophic to the standard sphere. The proof is inspired by the positive mass theorem on spin manifolds by Ammann-Humbert.

Mots clés: Paneitz-Branson operator; positive mass theorem

Domaines: Géométrie différentielle [math.DG]

Emmanuel Humbert, Simon Raulot. Positive mass theorem for the Paneitz-Branson operator. Calculus of Variations and Partial Differential Equations, 2009, 36 (4), pp.525-531. ⟨10.1007/s00526-009-0241-6⟩. ⟨hal-00297324⟩