Constant \(Q\)-curvature metrics in arbitrary dimension

DOI10.1016/j.jfa.2007.06.008zbMath1130.53027OpenAlexW2004282850MaRDI QIDQ2460013

Cheikh Birahim Ndiaye

Publication date: 14 November 2007

Published in: Journal of Functional Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jfa.2007.06.008

zbMATH Keywords

critical point theorygeneralized Yamabe problems

Mathematics Subject Classification ID

Elliptic equations on manifolds, general theory (58J05) Pseudodifferential and Fourier integral operators on manifolds (58J40) Methods of global Riemannian geometry, including PDE methods; curvature restrictions (53C21)

Related Items (40)

Constant \(Q\)-curvature metrics on conic 4-manifolds ⋮ Prescribing \(Q\)-curvature problem on \(S^n\) ⋮ Normal conformal metrics on \(\mathbb{R}^4\) with singular \(Q\)-curvature having power-like growth ⋮ Classification of solutions to the higher order Liouville's equation on \({\mathbb{R}^{2m}}\) ⋮ Liouville conformal field theory on even-dimensional spheres ⋮ Classification and a priori estimates for the singular prescribing \(Q\)-curvature equation on 4-manifold ⋮ The Nirenberg problem and its generalizations: a unified approach ⋮ On the prescribed \(Q\)-curvature problem in Riemannian manifolds ⋮ The nonlocal Liouville-type equation in \(\mathbb {R}\) and conformal immersions of the disk with boundary singularities ⋮ Singular limits in higher order Liouville-type equations ⋮ Results of prescribing \(Q\)-curvature on \(S^{n}\) ⋮ Elliptic equation with critical and negative exponents involving the GJMS operator on compact Riemannian manifolds ⋮ Topological methods for the resonant \(Q\)-curvature problem in arbitrary even dimension ⋮ Prescribed \(Q\)-curvature flow on \(S^n\) ⋮ Existence and compactness of conformal metrics on the plane with unbounded and sign-changing Gaussian curvature ⋮ Bubbling solutions of fourth order mean field equations on \(\mathbb{S}^4\) ⋮ Optimal control for the Paneitz obstacle problem ⋮ \(Q\)-curvature flow on 4-manifolds with boundary ⋮ The \(Q\)-curvature on a 4-dimensional Riemannian manifold \((M,g)\) with \(\int_M QdV_g = 8\pi^2\) ⋮ Conformal metrics on \(\mathbb R^{2m}\) with constant \(Q\)-curvature and large volume ⋮ Scalar curvature and \(Q\)-curvature of random metrics ⋮ Extremal functions for Moser-Trudinger type inequality on compact closed 4-manifolds ⋮ QUANTIZATION FOR THE PRESCRIBED Q-CURVATURE EQUATION ON OPEN DOMAINS ⋮ Gluing metrics with prescribed $Q$-curvature and different asymptotic behaviour in high dimension ⋮ Toward best isoperimetric constants for \((H^1,BMO)\)-normal conformal metrics on \(\mathbb R^n,n\geqslant 3\) ⋮ \(Q\)-curvature flow for GJMS operators with non-trivial kernel ⋮ An upper bound of the total Q-curvature and its isoperimetric deficit for higher-dimensional conformal Euclidean metrics ⋮ Examples of Einstein manifolds in odd dimensions ⋮ Existence of solutions to a higher dimensional mean-field equation on manifolds ⋮ Gaussian free fields and KPZ relation in \(\mathbb{R}^4\) ⋮ Concentration phenomena for the fractional Q‐curvature equation in dimension 3 and fractional Poisson formulas ⋮ Constant \(Q\)-curvature metrics near the hyperbolic metric ⋮ Concentration-compactness phenomena in the higher order Liouville's equation ⋮ Prescribed \(Q\)-curvature flow on closed manifolds of even dimension ⋮ The profile of bubbling solutions of a class of fourth order geometric equations on 4-manifolds ⋮ Concentration phenomena to a higher order Liouville equation ⋮ Algebraic topological methods for the supercritical \(Q\)-curvature problem ⋮ Constant 𝑄-curvature metrics with a singularity ⋮ Positive energy theorems in fourth-order gravity ⋮ A positive energy theorem for fourth-order gravity

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