A note on the uniqueness of solutions for the Yamabe problem

DOI10.1090/S0002-9939-2012-11284-5zbMath1273.53043arXiv1102.2321OpenAlexW1968677927MaRDI QIDQ2846859

Paolo Piccione, Levi Lopes de Lima, Michela Zedda

Publication date: 3 September 2013

Published in: Proceedings of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1102.2321

zbMATH Keywords

compactnessspace of solutions

Mathematics Subject Classification ID

Special Riemannian manifolds (Einstein, Sasakian, etc.) (53C25) Critical metrics (58E11)

Related Items (15)

Metrics of constant scalar curvature on sphere bundles ⋮ Bifurcation and local rigidity of homogeneous solutions to the Yamabe problem on spheres ⋮ Multiplicity of constant scalar curvature metrics in \(\mathbb{T}^k \times M\) ⋮ Harmonically free group actions and equivariant bifurcation in the Yamabe problem ⋮ Prescribing Morse Scalar Curvatures: Pinching and Morse Theory ⋮ Degenerate solutions of a nonlinear elliptic equation on the sphere ⋮ Multiplicity results for the Yamabe equation by Lusternik-Schnirelmann theory ⋮ A remark on the poroelastic center of dilation ⋮ Constant scalar curvature metrics on Hirzebruch surfaces ⋮ The Lichnerowicz and Obata first eigenvalue theorems and the Obata uniqueness result in the Yamabe problem on CR and quaternionic contact manifolds ⋮ On the bifurcation of solutions of the Yamabe problem in product manifolds with minimal boundary ⋮ The conformal Yamabe constant of product manifolds ⋮ Uniqueness of solutions of the Yamabe problem on manifolds with boundary ⋮ Solutions of the Yamabe equation by Lyapunov-Schmidt reduction ⋮ Sign-changing blow-up for the Yamabe equation at the lowest energy level

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• Compactness of solutions to the Yamabe problem. II
• Blow-up phenomena for the Yamabe equation
• Metrics of constant scalar curvature conformal to Riemannian products
• Recent progress on the Yamabe problem

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