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Masse des op\'erateurs GJMS
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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 $P_2$, 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.
Forward citations
Cited by 2 Pith papers
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Extremising eigenvalues of the GJMS operators in a fixed conformal class
Conformal eigenvalue extremals for GJMS operators of any order s and any index k exist under a gap condition for positive eigenvalues and unconditionally for negative eigenvalues, assuming a unique continuation property.
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A new boundary mass for asymptotically flat half-manifolds
Introduces a boundary analogue of the Gauss-Bonnet-Chern mass for asymptotically flat half-manifolds, proves it is well-defined, establishes positive mass theorems for graphical and conformally flat graphs, and provid...
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