Isoparametric hypersurfaces and metrics of constant scalar curvature

GUILLERMO HENRY; JIMMY PETEAN

ASIAN JOURNAL OF MATHEMATICS

INT PRESS BOSTON, INC

Año: 2014 vol. 18 p. 53 - 68

1093-6106

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