Vanishing of the residue Q-curvature at zero

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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 N≥1N\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.

References

Primary source

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

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