Q curvature on a class of manifolds with dimension at least 5

Abstract

For a smooth compact Riemannian manifold with positive Yamabe invariant, positive Q curvature and dimension at least 5, we prove the existence of a conformal metric with constant Q curvature. Our approach is based on the study of extremal problem for a new functional involving the Paneitz operator.

Material reorganized. References updated. To appear in Comm. Pure. Appl. Math

References in corpus (4)

• A Quartic Conformally Covariant Differential Operator for Arbitrary Pseudo-Riemannian Manifolds (Summary)
• Sign of Green's function of Paneitz operators and the Q curvature
• Asymptotic analysis for fourth order Paneitz equations with critical growth
• Lectures on the fourth order Q curvature equation

Cited by in corpus (9)

• Hardy-Littlewood-Sobolev inequalities on compact Riemannian manifolds and applications
• Singular solutions for the constant $Q$-curvature problem
• Nonuniqueness of conformal metrics with constant $Q$-curvature
• Lectures on the fourth order Q curvature equation
• Constant Q-curvature metrics with Delaunay ends: the nondegenerate case
• The Nirenberg problem and its generalizations: A unified approach
• Paneitz operator for metrics near $S^3$
• Riemannian manifolds with positive Yamabe invariant and Paneitz operator
• A nonlocal $\mathbf{Q}$-curvature flow on a class of closed manifolds of dimension $\mathbf{n}\ge 5$