Joao Henrique Andrade
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October 25, 2022

PIMS Lounge (ESB 4133)
Vancouver, BC V6T 1Z2

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This talk addresses the moduli space of complete, conformally flat metrics metrics on a sphere with $k$ punctures having constant positive $Q$-curvature and positive scalar curvature. Previous work has shown  that such metrics admit an asymptotic expansion near each puncture, allowing one to define an asymptotic necksize of each singular point. We prove that any set in the moduli space such that the distances between distinct punctures and the asymptotic necksizes all remain bounded away from zero is sequentially compact, mirroring a theorem of D. Pollack about singular Yamabe metrics. Along the way, we define a radial Pohozaev invariant at each puncture and refine some a priori bounds of the conformal factor, which may be of independent interest.

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October 25, 2022


PIMS Lounge (ESB 4133)

Vancouver, BC, CA
V6T 1Z2

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