Some existence results for the Webster scalar curvature problem in presence of symmetry

DOI10.1007/s10231-004-0101-0zbMath1105.35031arXivmath/0212143OpenAlexW2111308764MaRDI QIDQ2505613

Francesco Uguzzoni, Veronica Felli

Publication date: 27 September 2006

Published in: Annali di Matematica Pura ed Applicata. Serie Quarta (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0212143

zbMATH Keywords

Heisenberg groupWebster curvaturesubelliptic equations

Mathematics Subject Classification ID

Nonlinear elliptic equations (35J60) Methods of global Riemannian geometry, including PDE methods; curvature restrictions (53C21) Variational methods for second-order elliptic equations (35J20) Analysis on other specific Lie groups (43A80) Subelliptic equations (35H20)

Related Items (22)

Multiple non-negative solutions to a semilinear equation on Heisenberg group with indefinite nonlinearity ⋮ Prescribed Webster scalar curvature on \(S^{2n+1}\) in the presence of reflection or rotation symmetry ⋮ The Webster scalar curvature problem on the three dimensional CR manifolds ⋮ Hardy-Sobolev extremals, hyperbolic symmetry and scalar curvature equations ⋮ On the webster scalar curvature problem on the CR sphere with a cylindrical-type symmetry ⋮ Perturbation of Yamabe equation on Iwasawa \(N\) groups in presence of symmetry ⋮ The impact of the flatness condition on the prescribed webster scalar curvature ⋮ Methods of the theory of critical points at infinity on Cauchy Riemann manifolds ⋮ CR Nirenberg problem and zero Wester scalar curvature ⋮ The Webster scalar curvature revisited: The case of the three dimensional \(C R\) sphere ⋮ Existence and multiplicity results for the prescribed Webster scalar curvature problem on three CR manifolds ⋮ Prescribing the Webster scalar curvature on CR spheres ⋮ The Webster scalar curvature flow on CR sphere. I ⋮ The Webster scalar curvature flow on CR sphere. II ⋮ Multiplicity results for the prescribed webster scalar curvature on the three CR sphere under ``flatness condition ⋮ Optimal control in prescribing Webster scalar curvatures on 3-dimensional pseudo Hermitian manifolds ⋮ The {\(\beta\)}-flatness condition in CR spheres ⋮ Existence results for critical semi-linear equations on Heisenberg group domains ⋮ Topological methods for the prescribed Webster scalar curvature problem on CR manifolds ⋮ Hardy-Sobolev inequalities and hyperbolic symmetry ⋮ Prescribing Webster scalar curvature on CR manifolds of negative conformal invariants ⋮ Prescribed Webster scalar curvatures on compact pseudo-Hermitian manifolds

Cites Work

• CR Yamabe conjecture -- the conformally flat case.
• The concentration-compactness principle in the calculus of variations. The limit case. I
• The concentration-compactness principle in the calculus of variations. The limit case. II
• The Yamabe problem on CR manifolds
• Intrinsic CR normal coordinates and the CR Yamabe problem
• A perturbation result in prescribing scalar curvature on \(S^ n\)
• Pseudo-hermitian structures on a real hypersurface
• A variational approach to the equation \({\triangle}u+Ku^{{n+2}/{n- 2}}=0\) in \(\mathbb{R}^ n\)
• 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
• A perturbation result for the Webster scalar curvature problem on the CR sphere.
• A note on Yamabe-type equations on the Heisenberg group
• Positive solutions of Yamabe-type equations on the Heisenberg group
• Estimates for the \documentclass{article}\pagestyle{empty}\begin{document}$ \mathop \partial \limits^ - _b $\end{document} complex and analysis on the heisenberg group
• Variational perturbative methods and bifurcation of bound states from the essential spectrum
• On positive entire solutions to the Yamabe-type problem on the Heisenberg and stratified groups
• On the symmetric scalar curvature problem on \(S^n\)
• The CR Yamabe conjecture. The case \(n=1\)
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