Isoparametric Functions and Solutions of Yamabe Type Equations on Manifolds with Boundary

JUAN ZUCCOTTI; GUILLERMO HENRY

THE JOURNAL OF GEOMETRIC ANALYSIS

SPRINGER

Año: 2023 vol. 34

1050-6926

Let $(M,g)$ be a compact Riemannian manifold with non-empty boundary. Provided that $f$ is an isoparametric function of $(M,g)$, we prove existence results for positive solutions of the Yamabe equation that are constant along the level sets of $f$.If $(M,g)$ has positive constant scalar curvature, minimal boundary and admits an isoparametric function we also prove multiplicity results for positive solutions of the Yamabe equation on $(M imes N,g+th) $ where $(N,h)$ is any closed Riemannian manifold with positive constant scalar curvature.