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• W2228311586 abstract "In this paper we consider Riemannian manifolds $(M^n,g)$ of dimension $n geq 5$, with semi-positive $Q$-curvature and non-negative scalar curvature. Under these assumptions we prove (i) the Paneitz operator satisfies a strong maximum principle; (ii) the Paneitz operator is a positive operator; and (iii) its Green's function is strictly positive. We then introduce a non-local flow whose stationary points are metrics of constant positive $Q$-curvature. Modifying the test function construction of Esposito-Robert, we show that it is possible to choose an initial conformal metric so that the flow has a sequential limit which is smooth and positive, and defines a conformal metric of constant positive $Q$-curvature." @default.
• W2228311586 created "2016-06-24" @default.
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• W2228311586 date "2015-01-01" @default.
• W2228311586 modified "2023-10-01" @default.
• W2228311586 title "A strong maximum principle for the Paneitz operator and a non-local flow for the $Q$-curvature" @default.
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• W2228311586 doi "https://doi.org/10.4171/jems/553" @default.
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