Masse des opérateurs GJMS

2010/12/20 by Benoît Michel, Michel, Benoît
Computer Science · Mathematics · #35J08 #53A30 (Primary) 58J60 #53C21 (Secondary) #Advanced Mathematical Modeling in Engineering #Advanced Mathematical Physics Problems #Differential Geometry (math.DG) #FOS: Mathematics #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.1012.4414

openalex publication_date 2010/12/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

This work generalizes a construction by Habermann and Jost of a canonical metric in a Yamabe-positive conformal class, which uses the Green function of the conformal Laplacian. In dimension n=2k+1, 2k+2, or 2k+3, if the k-th GJMS operator P_k admits a Green function, the constant term of its singularity is shown to be a conformal density of weight 2k-n, when restricted to appropriate choices of conformal factor. When it is positive, it is used to build a canonical metric in the conformal class. In the case of the Paneitz-Branson operator P₂, in dimension 5, 6 or 7, we show a positiveness result. In additition, we relate it to an asymptotic invariant of the manifold obtained by stereographic projection via the Green function.

Citations

• The mass of an asymptotically flat manifold

Related

• On conformally covariant powers of the Laplacian
• A construction of critical GJMS operators using Wodzicki's residue
• Riemannian manifolds with positive Yamabe invariant and Paneitz operator
• Admissible Q-curvatures under isometries for the conformal GJMS operators
• Boundary operators associated to the sixth-order GJMS operator