On bifurcation of solutions of the Yamabe problem in product manifolds

DOI10.1016/j.anihpc.2011.10.005zbMath1239.58005arXiv1012.1497OpenAlexW2962760411MaRDI QIDQ413665

Michela Zedda, Paolo Piccione, Levi Lopes de Lima

Publication date: 7 May 2012

Published in: Annales de l'Institut Henri Poincaré. Analyse Non Linéaire (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1012.1497

zbMATH Keywords

Yamabe problembifurcation theorylocal rigiditymultiplicity of constant scalar curvature metricsproducts of compact manifolds

Mathematics Subject Classification ID

Critical metrics (58E11) Group-invariant bifurcation theory in infinite-dimensional spaces (58E09)

Related Items (26)

Metrics of constant scalar curvature on sphere bundles ⋮ Infinitely many solutions to the Yamabe problem on noncompact manifolds ⋮ Bifurcation of metrics with null scalar curvature and constant mean curvature on the boundary of compact manifolds ⋮ Bifurcation and local rigidity of homogeneous solutions to the Yamabe problem on spheres ⋮ Bifurcation for the constant scalar curvature equation and harmonic Riemannian submersions ⋮ Multipeak solutions for the Yamabe equation ⋮ Multiplicity of solutions to the Yamabe equation on warped products ⋮ Multiplicity of constant scalar curvature metrics in \(\mathbb{T}^k \times M\) ⋮ Nonuniqueness for a fully nonlinear boundary Yamabe-type problem via bifurcation theory ⋮ Multiplicity of singular solutions to the fractional Yamabe problem on spheres ⋮ Invariant solutions of the Yamabe equation on the Koiso-Cao soliton ⋮ Harmonically free group actions and equivariant bifurcation in the Yamabe problem ⋮ Singular CR structures of constant Webster curvature and applications ⋮ Global bifurcation techniques for Yamabe type equations on Riemannian manifolds ⋮ Degenerate solutions of a nonlinear elliptic equation on the sphere ⋮ Multiplicity results for the Yamabe equation by Lusternik-Schnirelmann theory ⋮ The mass of an asymptotically hyperbolic manifold with a non-compact boundary ⋮ A note on solutions of Yamabe-type equations on products of spheres ⋮ On the bifurcation of solutions of the Yamabe problem in product manifolds with minimal boundary ⋮ Bifurcation and local rigidity of homogeneous solutions to the Yamabe problem on maximal flag manifolds ⋮ Uniqueness of solutions of the Yamabe problem on manifolds with boundary ⋮ The mass in terms of Einstein and Newton ⋮ Solutions of the Yamabe equation by Lyapunov-Schmidt reduction ⋮ The first eigenvalue of a homogeneous CROSS ⋮ A note on the uniqueness of solutions for the Yamabe problem ⋮ Nodal solutions of Yamabe-type equations on positive Ricci curvature manifolds

Cites Work

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• A compactness theorem for the Yamabe problem
• Symmetry and asymmetry: the method of moving spheres
• Conformal deformation of a Riemannian metric to constant scalar curvature
• Scalar curvature of a metric with unit volume
• Equations différentielles non linéaires et problème de Yamabe concernant la courbure scalaire
• A variational approach for compact homogeneous Einstein manifolds
• Nonuniqueness and high energy solutions for a conformally invariant scalar equation
• Remarks on conformal transformations
• Einstein manifolds
• A priori estimates for the Yamabe problem in the non-locally conformally flat case
• Le spectre d'une variété riemannienne. (The spectrum of a Riemannian manifold)
• The conjectures on conformal transformations of Riemannian manifolds
• Compactness of solutions to the Yamabe problem. II
• Certain conditions for a Riemannian manifold to be isometric with a sphere
• Bifurcation and symmetry-breaking
• Metrics of constant scalar curvature conformal to Riemannian products
• ON UNIQUENESS AND DIFFERENTIABILITY IN THE SPACE OF YAMABE METRICS
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