In this article we establish optimal estimates for the first eigenvalue of Schrödinger operators on the -dimensional unit sphere. These estimates depend on norms of the potential, or of its inverse, and are equivalent to interpolation inequalities on the sphere. We also characterize a semiclassical asymptotic regime and discuss how our estimates on the sphere differ from those on the Euclidean space.
"Spectral estimates on the sphere." Anal. PDE 7 (2) 435 - 460, 2014. https://doi.org/10.2140/apde.2014.7.435