A note on solutions of Yamabe-type equations on products of spheres

Petean, Jimmy; Barrantes González, Héctor

doi:10.1090/proc/14478

A note on solutions of Yamabe-type equations on products of spheres
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by Jimmy Petean and Héctor Barrantes González PDF

Proc. Amer. Math. Soc. 147 (2019), 3143-3153 Request permission

Abstract:

We consider Yamabe-type equations on the Riemannian product of constant curvature metrics on $\mathbf {S}^n \times \mathbf {S}^n$ and study solutions which are invariant by the cohomogeneity one diagonal action of $O(n+1)$. We obtain multiplicity results for both positive and nodal solutions. In particular we prove the existence of nodal solutions of the Yamabe equation on these products which depend non-trivially on both factors.

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