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On constant Q-curvature metrics with isolated singularities
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In this paper we derive a refined asymptotic expansion, near an isolated singularity, for conformally flat metrics with constant positive Q-curvature and positive scalar curvature. The condition that the metric has constant Q-curvature forces the conformal factor to satisfy a fourth order nonlinear partial differential equation with critical Sobolev growth, whose leading term is the bilaplacian. We model our results on a similar asymptotic expansion for conformally flat, constant scalar curvature metrics proven by Korevaar, Mazzeo, Pacard, and Schoen. Along the way we analyze the linearization of the Q-curvature equation about the Delaunay metrics recently discovered by Frank and K\"onig, which may be of independent interest.
Forward citations
Cited by 2 Pith papers
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Local asymptotics for singular solutions to critical Hartree equations
For the critical Hartree equation, positive singular solutions are claimed to be radially symmetric and to converge near the singularity to a blow-up limit, but the key lower-bound proof is missing.
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