CONSTRUCTION OF BLOW-UP SEQUENCES FOR THE PRESCRIBED SCALAR CURVATURE EQUATION ON Sn I: UNIFORM CANCELLATION

DOI10.1142/S0219199712500083zbMath1275.53039OpenAlexW2069733644MaRDI QIDQ5388165

Man-Chun Leung

Publication date: 18 April 2012

Published in: Communications in Contemporary Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1142/s0219199712500083

zbMATH Keywords

Sobolev spacesblow-upcritical pointsscalar curvature equation

Mathematics Subject Classification ID

Sobolev spaces and other spaces of ``smooth functions, embedding theorems, trace theorems (46E35) Nonlinear elliptic equations (35J60) Methods of global Riemannian geometry, including PDE methods; curvature restrictions (53C21)

Related Items (6)

Conformal scalar curvature equation on Sn: Functions with two close critical points (Twin Pseudo-Peaks) ⋮ Construction of blow-up sequences for the prescribed scalar curvature equation on \(S^n\). III: Aggregated and towering blow-ups ⋮ Refined estimates for simple blow-ups of the scalar curvature equation on $S^n$ ⋮ Prescribing Morse Scalar Curvatures: Pinching and Morse Theory ⋮ Prescribed scalar curvature equation on $S^n$ in the presence of reflection or rotation symmetry ⋮ Compactness and non-compactness for Yamabe-type problems

Cites Work

• The scalar-curvature problem on the standard three-dimensional sphere
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• Blow-up phenomena for the Yamabe equation. II
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• Estimate of the conformal scalar curvature equation via the method of moving planes. II
• Perturbation of \(\Delta u+u^{(N+2)/(N-2)}=0\), the scalar curvature problem in \(\mathbb{R}^N\), and related topics
• Blow-up solutions of nonlinear elliptic equations in \(\mathbb{R}^n\) with critical exponent
• A note on the Kazdan-Warner type condition
• Prescribing scalar curvature on \(\mathbb{S}^ n\) and related problems. I
• The conjectures on conformal transformations of Riemannian manifolds
• Blow-up phenomena for the Yamabe equation
• Asymptotic symmetry and local behavior of semilinear elliptic equations with critical sobolev growth
• Estimates of the conformal scalar curvature equation via the method of moving planes
• Prescribing scalar curvature on Sn and related problems, part II: Existence and compactness
• On the symmetric scalar curvature problem on \(S^n\)

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