Isoparametric hypersurfaces and metrics of constant scalar curvature

Guillermo Henry; Jimmy Petean

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arXiv · 1103.0314

Isoparametric hypersurfaces and metrics of constant scalar curvature

Guillermo Henry·Jimmy Petean

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Abstract

We showed the existence of non-radial solutions of the equation $Δu -λu + λu^q =0$ on the round sphere $S^m$, for $q<2m/(m-2)$, and study the number of such solutions in terms of $λ$. We show that for any isoparametric hypersurface $M\subset S^m$ there are solutions such that $M$ is a regular level set (and the number of such solutions increases with $λ$). We also show similar results for isoparametric hypersurfaces in general Riemannian manifolds. These solutions give multiplicity results for metrics of constant scalar curvature on conformal classes of Riemannian products.

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BibTeX RIS

Guillermo Henry, Jimmy Petean. 2013-09-02. Isoparametric hypersurfaces and metrics of constant scalar curvature. https://arxiv.org/abs/1103.0314

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