Q-Curvature on a Class of Manifolds with Dimension at Least 5

DOI10.1002/cpa.21623zbMath1346.53037arXiv1411.3926OpenAlexW1938984303MaRDI QIDQ3185926

Feng Bo Hang, Paul C. Yang

Publication date: 8 August 2016

Published in: Communications on Pure and Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1411.3926

zbMATH Keywords

Paneitz operatorYamabe invariant\(Q\)-curvature

Mathematics Subject Classification ID

Global Riemannian geometry, including pinching (53C20)

Related Items (25)

Qualitative properties for solutions to subcritical fourth order systems* ⋮ Remarks on GJMS operator of order six ⋮ A note on prescribed Q-curvature ⋮ The Nirenberg problem and its generalizations: a unified approach ⋮ Paneitz operator for metrics near \(S^{3}\) ⋮ Existence theorems of the fractional Yamabe problem ⋮ Hardy-Littlewood-Sobolev inequalities on compact Riemannian manifolds and applications ⋮ Improved Beckner's inequality for axially symmetric functions on \(\mathbb{S}^4\) ⋮ Multiplicity of singular solutions to the fractional Yamabe problem on spheres ⋮ Improved higher-order Sobolev inequalities on CR sphere ⋮ Local estimates for conformal \(Q\)-curvature equations ⋮ Singular solutions for the constant \(Q\)-curvature problem ⋮ Compactness of conformal metrics with constant \(Q\)-curvature. I ⋮ Liouville type results for semilinear biharmonic problems in exterior domains ⋮ Asymptotic symmetry and local behavior of solutions of higher order conformally invariant equations with isolated singularities ⋮ A compactness theorem for the fractional Yamabe problem. I: The nonumbilic conformal infinity ⋮ Local behavior of positive solutions of higher order conformally invariant equations with a singular set ⋮ A compactness theorem on Branson's \(Q\)-curvature equation ⋮ Minimal energy solutions to the fractional Lane-Emden system: existence and singularity formation ⋮ Improved Beckner's inequality for axially symmetric functions on \(\mathbb{S}^n\) ⋮ The effect of pinching conditions in prescribing \(Q\)-curvature on standard spheres ⋮ Existence of conformal metrics with prescribed Q-curvature on manifolds ⋮ Positive energy theorems in fourth-order gravity ⋮ Connected sum construction of constant \(Q\)-curvature manifolds in higher dimensions ⋮ A positive energy theorem for fourth-order gravity

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• \(Q\)-curvature flow for GJMS operators with non-trivial kernel
• A strong maximum principle for the Paneitz operator and a non-local flow for the \(\mathcal Q\)-curvature
• Sharp constants in the Hardy-Littlewood-Sobolev and related inequalities
• The concentration-compactness principle in the calculus of variations. The limit case. I
• An integral equation in conformal geometry
• Positive mass theorem for the Paneitz-Branson operator
• Conformal deformation of a Riemannian metric to constant scalar curvature
• Conformally flat manifolds, Kleinian groups and scalar curvature
• Mountain pass critical points for Paneitz-Branson operators.
• Paneitz-type operators and applications
• Positivity of Paneitz operators
• An equation of Monge-Ampère type in conformal geometry, and four-manifolds of positive Ricci curvature
• The Sobolev inequality for Paneitz operator on three manifolds
• Extremal metrics of zeta function determinants on 4-manifolds
• Existence of conformal metrics with constant \(Q\)-curvature
• Paneitz operator for metrics near \(S^{3}\)
• Compactness for conformal metrics with constant \(Q\) curvature on locally conformally flat manifolds
• Riemannian Manifolds with Positive Yamabe Invariant and Paneitz Operator
• QCurvature on a Class of 3-Manifolds
• LECTURES ON THE FOURTH-ORDER Q CURVATURE EQUATION
• Asymptotic analysis for fourth order Paneitz equations with critical growth
• On positive solutions to semilinear conformally invariant equations on locally conformally flat manifolds
• Sign of Green's Function of Paneitz Operators and theQCurvature
• Differential operators cononically associated to a conformal structure.
• The Yamabe problem
• On a Fourth Order Equation in 3-D
• Compactness and global estimates for the geometric Paneitz equation in high dimensions
• Sharp integral inequalities for harmonic functions
• On the Paneitz energy on standard three sphere
• Classification of solutions for an integral equation

This page was built for publication: Q-Curvature on a Class of Manifolds with Dimension at Least 5