Multiplicity results for the Yamabe equation by Lusternik-Schnirelmann\n theory

2016/11/03 by Jimmy Petean, Petean, Jimmy · 1 citation
Mathematics · Physics and Astronomy · #Geometric Analysis and Curvature Flows #Black Holes and Theoretical Physics #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.1611.01177

Abstract

Let (M,g) be any closed Riemannianan manifold and (N,h) be a Riemannian\nmanifold of constant positive scalar curvature. We prove that the Yamabe\nequation on the Riemannian product (M\× N , g + \δ h) has at least\nCat(M) +1 solutions for \δ small enough, where Cat(M) denotes the\nLusternik-Schnirelmann-category of M. Cat(M) of the solutions obtained have\nenergy arbitrarily close to the minimum.\n

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• Multiplicity of solutions for Gross-Pitaevskii equations on Riemannian manifolds

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