The axisymmetric \(\sigma_k\)-Nirenberg problem

DOI10.1016/j.jfa.2021.109198zbMath1478.35119arXiv2106.04504OpenAlexW3183857692MaRDI QIDQ1982528

Bo Wang, Luc Nguyen, Yan-yan Li

Publication date: 14 September 2021

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

Full work available at URL: https://arxiv.org/abs/2106.04504

zbMATH Keywords

axisymmetryexistence and non-existence\(\sigma_k\)-curvaturecompactness and non-compactness

Mathematics Subject Classification ID

Nonlinear elliptic equations (35J60) A priori estimates in context of PDEs (35B45) Elliptic equations on manifolds, general theory (58J05)

Related Items (6)

A Liouville-type theorem for fully nonlinear CR invariant equations on the Heisenberg group ⋮ On the \(\sigma_2\)-Nirenberg problem on \(\mathbb{S}^2\) ⋮ A Liouville's theorem for some Monge-Ampère type equations ⋮ Differential inclusions for the Schouten tensor and nonlinear eigenvalue problems in conformal geometry ⋮ Nonexistence results of solutions of parabolic-type equations and systems on the Heisenberg group ⋮ A Liouville theorem for Möbius invariant equations

Cites Work

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• On the prescribing \(\sigma_2\) curvature equation on \(\mathbb S^4\)
• Degenerate conformally invariant fully nonlinear elliptic equations
• Symmetry and asymmetry: the method of moving spheres
• The Dirichlet problem for nonlinear second order elliptic equations. III: Functions of the eigenvalues of the Hessian
• An ODE approach to the equation \(\Delta u + Ku^{{n+2}\over{n-2}}=0\) in \(\mathbb{R}^ n\)
• Estimate of the conformal scalar curvature equation via the method of moving planes. II
• Prescribing scalar curvature on \(\mathbb{S}^ n\) and related problems. I
• Conformal geometry, contact geometry, and the calculus of variations
• A Kazdan-Warner type identity for the \(\sigma_{k}\) curvature
• A priori estimates and existence for a class of fully nonlinear elliptic equations in conformal geometry
• On some conformally invariant fully nonlinear equations. II: Liouville, Harnack and Yamabe
• Harnack Inequalities and Bôcher-Type Theorems for Conformally Invariant, Fully Nonlinear Degenerate Elliptic Equations
• Positive solutions of nonlinear elliptic equations involving critical sobolev exponents
• Degree Theory for Second Order Nonlinear Elliptic Operators and its Applications
• Blowing up with infinite energy of conformal metrics on Sⁿ
• On some conformally invariant fully nonlinear equations
• Non-existence and symmetry of solutions to the scalar curvature equation
• Prescribing scalar curvature on Sn and related problems, part II: Existence and compactness
• Some Remarks on Singular Solutions of Nonlinear Elliptic Equations III: Viscosity Solutions Including Parabolic Operators
• Local gradient estimates of solutions to some conformally invariant fully nonlinear equations
• On axisymmetric solutions of the conformal scalar curvature equation on \(S^n\)

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