Asian Journal of Mathematics
- Asian J. Math.
- Volume 18, Number 1 (2014), 53-68.
Isoparametric hypersurfaces and metrics of constant scalar curvature
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 $q \lt (m + 2)/ (m - 2)$, and study the number of such solutions in terms of $\lambda$. 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 $\lambda$). 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.
Asian J. Math., Volume 18, Number 1 (2014), 53-68.
First available in Project Euclid: 27 August 2014
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Henry, Guillermo; Petean, Jimmy. Isoparametric hypersurfaces and metrics of constant scalar curvature. Asian J. Math. 18 (2014), no. 1, 53--68. https://projecteuclid.org/euclid.ajm/1409168512