Geodesic
A strong maximum principle for the Paneitz operator and a non-local flow for the $Q$-curvature
Journal of the European Mathematical Society, Tome 17 (2015) no. 9, pp. 2137-2173 Cet article a éte moissonné depuis la source EMS Press

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In this paper we consider Riemannian manifolds (Mn,g) of dimension n≥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.
DOI : 10.4171/jems/553
Classification : 35-XX
Keywords: Q-curvature, Paneitz operator, conformal geometry, non-local flow 
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     title = {A strong maximum principle for the {Paneitz} operator and a non-local flow for the $Q$-curvature},
     journal = {Journal of the European Mathematical Society},
     pages = {2137--2173},
     year = {2015},
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Matthew J. Gursky; Andrea Malchiodi. A strong maximum principle for the Paneitz operator and a non-local flow for the $Q$-curvature. Journal of the European Mathematical Society, Tome 17 (2015) no. 9, pp. 2137-2173. doi: 10.4171/jems/553

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