On the symmetric scalar curvature problem on \(S^n\)

DOI10.1006/jdeq.2000.3816zbMath1006.35044OpenAlexW2045042268MaRDI QIDQ5929884

Antonio Ambrosetti, Andrea Malchiodi

Publication date: 17 April 2001

Published in: Journal of Differential Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1006/jdeq.2000.3816

zbMATH Keywords

symmetryexistencescalar curvature problem

Mathematics Subject Classification ID

Methods of global Riemannian geometry, including PDE methods; curvature restrictions (53C21) Elliptic equations and elliptic systems (35J99)

Related Items (14)

PRESCRIBING A FOURTH ORDER CONFORMAL INVARIANT ON THE STANDARD SPHERE — PART I: A PERTURBATION RESULT ⋮ Hypersurfaces in \(\mathbb H^{n+1}\) and conformally invariant equations: the generalized Christoffel and Nirenberg problems ⋮ Scalar curvature equation on \(S^n\). I: Topological conditions ⋮ Scalar curvature equation on \(S^n\). II: Analytic characterizations ⋮ Construction of blow-up sequences for the prescribed scalar curvature equation on \(S^n\). II: Annular domains ⋮ Perturbative techniques in conformal geometry ⋮ A prescribed scalar curvature-type equation: Almost critical manifolds and multiple solutions. ⋮ CONSTRUCTION OF BLOW-UP SEQUENCES FOR THE PRESCRIBED SCALAR CURVATURE EQUATION ON Sⁿ I: UNIFORM CANCELLATION ⋮ Prescribed scalar curvature equation on $S^n$ in the presence of reflection or rotation symmetry ⋮ Bifurcation results for a fractional elliptic equation with critical exponent in \(\mathbb {R}^n\) ⋮ Some existence results for the Webster scalar curvature problem in presence of symmetry ⋮ Multiplicity results for the Yamabe problem on S ⁿ ⋮ Multi-bump solutions and multi-tower solutions for equations on \(\mathbb R^N\) ⋮ Invariant conformal metrics on $\mathbb{S}^{n}$

Cites Work

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• The scalar-curvature problem on the standard three-dimensional sphere
• Conformal metrics with prescribed scalar curvature
• Scalar curvatures on \(S^ n\)
• Perturbation of \(\Delta u+u^{(N+2)/(N-2)}=0\), the scalar curvature problem in \(\mathbb{R}^N\), and related topics
• Homoclinics: Poincaré-Melnikov type results via a variational approach
• Homoclinics and chaotic behaviour for perturbed second order systems
• Prescribing scalar curvature on \(\mathbb{S}^ n\) and related problems. I
• On symmetric solutions of an elliptic equation with a nonlinearity involving critical Sobolev exponent
• Prescribing scalar curvature on Sn and related problems, part II: Existence and compactness

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