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Compactness for conformal metrics with Constant $Q$ curvature on locally conformally flat manifolds

Jie Qing·David Raske
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Abstract

In this note we study the conformal metrics of constant $Q$ curvature on closed locally conformally flat manifolds. We prove that for a closed locally conformally flat manifold of dimension $n\geq 5$ and with Poincarë exponent less than $\frac {n-4}2$, the set of conformal metrics of positive constant $Q$ and positive scalar curvature is compact in the $C^\infty$ topology.

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Jie Qing, David Raske. 2005-08-21. Compactness for conformal metrics with Constant $Q$ curvature on locally conformally flat manifolds. https://arxiv.org/abs/math/0508389

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