Vanishing of the residue Q-curvature at zero

Let DNres(λ){\bf D}_N^{res}(\lambda) be the residue family operator of order NN, and define the associated residue Q-curvature by

QNres(0):=DNres(0)(1).{\bf Q}_N^{res}(0):={\bf D}_N^{res}(0)(1).

Vanishing conjecture for residue Q-curvatures. For every N1N\ge 1,

QNres(0)=DNres(0)(1)=0.{\bf Q}_N^{res}(0)={\bf D}_N^{res}(0)(1)=0.

The case N=2N=2 is established immediately before the conjecture. The source describes the general assertion as open.

Sources & referencesView supporting material

Primary source

Andreas Juhl and Bent Orsted, “Residue families, singular Yamabe problems and extrinsic conformal Laplacians”, arXiv:2101.09027 (2022).

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