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A compactness theorem
on Branson's Q-curvature equation
Gang Li |
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Vol. 302 (2019), No. 1, 119–179
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Abstract |
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Let (M,g) be a closed Riemannian manifold of dimension 5≤n≤7. Assume that (M,g) is not conformally equivalent to the round sphere. If the scalar curvature Rg is greater than or equal to 0 and the Q-curvature Qg is greater than or equal to 0 on M with Qg(p)>0 for some point p∈M, we prove that the set of metrics in the conformal class of g with prescribed constant positive Q-curvature is compact in C4,α for any 0<α<1. |
Keywords
compactness, constant Q-curvature metrics, blowup
argument, positive mass theorem, maximum principle, fourth
order elliptic equations
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Mathematical Subject Classification 2010
Primary: 53C21
Secondary: 35B50, 35J61, 53A30
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Milestones
Received: 21 December 2017
Revised: 4 January 2019
Accepted: 13 March 2019
Published: 5 November 2019
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Authors |
| Gang Li | |
| Beijing International Center for
Mathematical Research Peking University Beijing China |
Department of Mathematics Shandong University Ji’an China |
