Algebraic topological methods for the supercritical \(Q\)-curvature problem

DOI10.1016/j.aim.2015.03.002zbMath1312.53062OpenAlexW2003906139WikidataQ125915592 ScholiaQ125915592MaRDI QIDQ2342654

Cheikh Birahim Ndiaye

Publication date: 29 April 2015

Published in: Advances in Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.aim.2015.03.002

zbMATH Keywords

Morse theory\(Q\)-curvaturecritical points at infinityConley theoryalgebraic topological methods

Mathematics Subject Classification ID

Relations of PDEs with special manifold structures (Riemannian, Finsler, etc.) (58J60) Methods of global Riemannian geometry, including PDE methods; curvature restrictions (53C21) Generic properties, structural stability of dynamical systems (37C20) Singular homology and cohomology theory (55N10)

Related Items (5)

Classification and a priori estimates for the singular prescribing \(Q\)-curvature equation on 4-manifold ⋮ ``Large conformal metrics of prescribed \(Q\)-curvature in the negative case ⋮ Topological methods for the resonant \(Q\)-curvature problem in arbitrary even dimension ⋮ Optimal control for the Paneitz obstacle problem ⋮ Prescribed \(Q\)-curvature flow on closed manifolds of even dimension

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• \(Q\)-curvature and Poincaré metrics
• A quartic conformally covariant differential operator for arbitrary pseudo-Riemannian manifolds (Summary)
• An upper bound of the total Q-curvature and its isoperimetric deficit for higher-dimensional conformal Euclidean metrics
• Constant t-curvature conformal metrics on 4-manifolds with boundary
• Conformal metrics with constant \(Q\)-curvature for manifolds with boundary
• Morse theory and a scalar field equation on compact surfaces
• The profile of bubbling solutions of a class of fourth order geometric equations on 4-manifolds
• Periodic solutions of Hamiltonian systems of 3-body type
• Estimates and extremals for zeta function determinants on four-manifolds
• On conformal deformations of metrics on \(S^n\)
• Conformal normal coordinates
• The zeta functional determinants on manifolds with boundary. I: The formula
• The zeta functional determinants on manifolds with boundary. II: Extremal metrics and compactness of isospectral set
• Algebraic topology methods for the prescribed scalar curvature problem
• A topological hypothesis for the prescribed scalar curvature problem
• Global existence and convergence for a higher order flow in conformal geometry
• Ambient metric construction of \(Q\)-curvature in conformal and CR geometries
• On the Chern-Gauss-Bonnet integral for conformal metrics on \(\mathbb{R}^4\)
• Compactification of a class of conformally flat 4-manifold
• A fully nonlinear equation on four-manifolds with positive scalar curvature.
• An equation of Monge-Ampère type in conformal geometry, and four-manifolds of positive Ricci curvature
• A conformally invariant sphere theorem in four dimensions
• Extremal metrics of zeta function determinants on 4-manifolds
• An invariant for Yamabe-type flows with applications to scalar-curvature problems in high dimension
• The principal eigenvalue of a conformally invariant differential operator, with an application to semilinear elliptic PDE
• Existence of conformal metrics with constant \(Q\)-curvature
• Constant \(Q\)-curvature metrics in arbitrary dimension
• Extremal functions for Moser-Trudinger type inequality on compact closed 4-manifolds
• Conformal metrics with constant \(Q\)-curvature
• \(Q\)-curvature flow on \(S^4\)
• \(Q\)-curvature flow on 4-manifolds
• Symmetric Joins and Weighted Barycenters
• The Existence of Generalized Isothermal Coordinates for Higher Dimensional Riemannian Manifolds
• Conformally Invariant Powers of the Laplacian, I: Existence
• Differential operators cononically associated to a conformal structure.
• On a nonlinear elliptic equation involving the critical sobolev exponent: The effect of the topology of the domain
• Explicit Functional Determinants in Four Dimensions
• Isolated Invariant Sets and Isolating Blocks
• Integral pinching results for manifolds with boundary
• Regularity of weak solutions to critical exponent variational equations

This page was built for publication: Algebraic topological methods for the supercritical \(Q\)-curvature problem