Multiplicity of solutions to the Yamabe problem on collapsing Riemannian submersions

DOI10.2140/pjm.2013.266.1zbMath1287.53030arXiv1304.5510OpenAlexW1974939657WikidataQ115230589 ScholiaQ115230589MaRDI QIDQ388794

Paolo Piccione, Renato G. Bettiol

Publication date: 7 January 2014

Published in: Pacific Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1304.5510

zbMATH Keywords

Yamabe problemRiemannian submersionsequivariant bifurcationCheeger deformationconstant scalar curvature metricshomogeneous fibration

Mathematics Subject Classification ID

Differential geometry of homogeneous manifolds (53C30) Spectral problems; spectral geometry; scattering theory on manifolds (58J50) Global Riemannian geometry, including pinching (53C20) Methods of global Riemannian geometry, including PDE methods; curvature restrictions (53C21) Applications of variational problems in infinite-dimensional spaces to the sciences (58E50) Bifurcation theory for PDEs on manifolds (58J55)

Related Items

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 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 \(\mathbb{T}^k \times M\) ⋮ A variational analysis of the spinorial Yamabe equation on product manifolds ⋮ Harmonically free group actions and equivariant bifurcation in the Yamabe problem ⋮ Global bifurcation techniques for Yamabe type equations on Riemannian manifolds ⋮ Multiplicity results for the Yamabe equation by Lusternik-Schnirelmann theory ⋮ 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 ⋮ Solutions of the Yamabe equation by Lyapunov-Schmidt reduction ⋮ The first eigenvalue of a homogeneous CROSS ⋮ Nodal solutions of Yamabe-type equations on positive Ricci curvature manifolds ⋮ Equivariant Bifurcation in Geometric Variational Problems ⋮ Slowly converging Yamabe flows