Multipeak solutions for the Yamabe equation

Rey, Carolina A.; Ruiz, Juan Miguel

doi:10.48550/arxiv.1807.08385

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2018

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“…The solutions provided in our theorem have low energy and they are close to the explicit approximate solutions. Rey and Ruiz [22] also applied the Lyapunov-Schmidt reduction technique to construct multipeak high-energy solutions under certain conditions on the scalar curvature of g. These seem to be the only known results when the scalar curvature of g is not a constant.…”

Section: Introductionmentioning

confidence: 99%

Solutions of the Yamabe Equation By Lyapunov-Schmidt Reduction

Dávila¹,

Munive²

2018

Preprint

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Given any closed Riemannian manifold (M, g) we use the Lyapunov-Schmidt finitedimensional reduction method to prove multiplicity results for positive solutions of a subcritical Yamabe type equation on (M, g). If (N, h) is a closed Riemannian manifold of constant positive scalar curvature our result gives multiplicity results for the Yamabe equation on the Riemannian product (M × N, g + ε 2 h), for ε > 0 small.

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Section: Introductionmentioning

confidence: 99%