Vol. 319, No. 1, 2022

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A note on prescribed Q-curvature

Mingxiang Li

Vol. 319 (2022), No. 1, 181–188

Let (M,g) be a compact Riemannian manifold of dimension 5 n 7 with nonnegative scalar curvature and semipositive Q-curvature. Assume (M,g) is not conformally equivalent to the standard sphere. If a prescribed positive smooth function f is flat up to n 4 order at some maximum point, there exists a conformal metric g~ = u4(n4)g such that Qg~ = f. This is a natural higher order version of the result of Escobar and Schoen (1986).

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prescribed Q-curvature, Paneitz operator
Mathematical Subject Classification
Primary: 35J35, 53C21
Received: 16 September 2021
Accepted: 4 June 2022
Published: 28 August 2022
Mingxiang Li
Department of Mathematics
Nanjing University