A strong maximum principle for the Paneitz operator and a non-local flow for the \(\mathcal Q\)-curvature

DOI10.4171/JEMS/553zbMath1330.35053arXiv1401.3216OpenAlexW2228311586MaRDI QIDQ747605

Andrea Malchiodi, Matthew J. Gursky

Publication date: 16 October 2015

Published in: Journal of the European Mathematical Society (JEMS) (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1401.3216

zbMATH Keywords

conformal geometryeponymous operator of Paneitz

Mathematics Subject Classification ID

Maximum principles in context of PDEs (35B50) Elliptic equations on manifolds, general theory (58J05)

Related Items (38)

Sign-changing solutions for elliptic problem involving the sixth order \textit{GJMS} operator on compact manifold ⋮ Compactness of conformally compact Einstein manifolds in dimension 4 ⋮ Q-Curvature on a Class of Manifolds with Dimension at Least 5 ⋮ Prescribing the \(Q\)-curvature problem on 6-dimensional manifolds ⋮ Deformation of the \(\sigma_2\)-curvature ⋮ 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 ⋮ ``Large conformal metrics of prescribed \(Q\)-curvature in the negative case ⋮ The Paneitz curvature problem on \(S^n\) ⋮ Quasiconformal flows on non-conformally flat spheres ⋮ Multiplicity of singular solutions to the fractional Yamabe problem on spheres ⋮ The trace and the mass of subcritical GJMS operators ⋮ Equivariant solutions to the optimal partition problem for the prescribed \(Q\)-curvature equation ⋮ Second-order Sobolev inequalities on a class of Riemannian manifolds with nonnegative Ricci curvature ⋮ Local estimates for conformal \(Q\)-curvature equations ⋮ Geometric inequalities for manifolds with Ricci curvature in the Kato class ⋮ Unnamed Item ⋮ Singular solutions for the constant \(Q\)-curvature problem ⋮ Compactness of conformal metrics with constant \(Q\)-curvature. I ⋮ The first GJMS invariant ⋮ Deformations of \(Q\)-curvature. I ⋮ Comparison theorems for GJMS operators ⋮ On a class of non-local operators in conformal geometry ⋮ Asymptotic symmetry and local behavior of solutions of higher order conformally invariant equations with isolated singularities ⋮ QCurvature on a Class of 3-Manifolds ⋮ A compactness theorem for the fractional Yamabe problem. I: The nonumbilic conformal infinity ⋮ GJMS-type operators on a compact Riemannian manifold: best constants and Coron-type solutions ⋮ On Fractional GJMS Operators ⋮ Local behavior of positive solutions of higher order conformally invariant equations with a singular set ⋮ A compactness theorem on Branson's \(Q\)-curvature equation ⋮ Nonhomogeneous polyharmonic elliptic problems involving GJMS operator on Riemannian manifold ⋮ 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

• The \(Q\)-curvature on a 4-dimensional Riemannian manifold \((M,g)\) with \(\int_M QdV_g = 8\pi^2\)
• A quartic conformally covariant differential operator for arbitrary pseudo-Riemannian manifolds (Summary)
• 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
• Equations différentielles non linéaires et problème de Yamabe concernant la courbure scalaire
• Mountain pass critical points for Paneitz-Branson operators.
• Paneitz-type operators and applications
• Extremal metrics of zeta function determinants on 4-manifolds
• The principal eigenvalue of a conformally invariant differential operator, with an application to semilinear elliptic PDE
• Best constant for the embedding of the space \(H^ 2\cap H^ 1_ 0(\Omega)\) into \(L^{2N/(N-4)}\Omega\)
• Existence of conformal metrics with constant \(Q\)-curvature
• \(Q\)-curvature flow on 4-manifolds
• On Fractional GJMS Operators
• 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
• Compactness and global estimates for the geometric Paneitz equation in high dimensions

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