Sign of Green's function of Paneitz operators and the Q curvature

Abstract

In a conformal class of metrics with positive Yamabe invariant, we derive a necessary and sufficient condition for the existence of metrics with positive Q curvature. The condition is conformally invariant. We also prove some inequalities between the Green's functions of the conformal Laplacian operator and the Paneitz operator.

Typos corrected

References in corpus (4)

• A Quartic Conformally Covariant Differential Operator for Arbitrary Pseudo-Riemannian Manifolds (Summary)
• Asymptotic analysis for fourth order Paneitz equations with critical growth
• Positive mass theorem for the Paneitz-Branson operator
• Paneitz operator for metrics near $S^3$

Cited by in corpus (17)

• Hardy-Littlewood-Sobolev inequalities on compact Riemannian manifolds and applications
• Existence theorems of the fractional Yamabe problem
• GJMS-type Operators on a compact Riemannian manifold: Best constants and Coron-type solutions
• Nonuniqueness of conformal metrics with constant $Q$-curvature
• Lectures on the fourth order Q curvature equation
• Q curvature on a class of manifolds with dimension at least 5
• Uniqueness of conformal metrics with constant Q-curvature on closed Einstein manifolds
• Prescribing integral curvature equation
• Deformations of Q-curvature II
• The Nirenberg problem and its generalizations: A unified approach
• Conformal Geometry on Four Manifolds
• Improved Sobolev inequality under constraints
• Energy in Fourth Order Gravity
• Riemannian manifolds with positive Yamabe invariant and Paneitz operator
• A perturbation approach for Paneitz energy on standard three sphere
• On the Positive Energy Theorem for Stationary Solutions to Fourth-Order Gravity
• A nonlocal $\mathbf{Q}$-curvature flow on a class of closed manifolds of dimension $\mathbf{n}\ge 5$