Full Laplace spectrum of distance spheres in symmetric spaces of rank one

BETTIOL, RENATO G.; LAURET, EMILIO A.; PICCIONE, PAOLO

BULLETIN OF THE LONDON MATHEMATICAL SOCIETY

OXFORD UNIV PRESS

Año: 2022 vol. 54 p. 1683 - 1704

0024-6093

We use Lie-theoretic methods to explicitly compute the full spectrum of the Laplace--Beltrami operator on homogeneous spheres which occur as geodesic distance spheres in (compact or noncompact) symmetric spaces of rank one, and provide a single unified formula for all cases. As an application, we find all resonant radii for distance spheres in the compact case, i.e., radii where there is bifurcation of embedded constant mean curvature spheres, and show that distance spheres are stable and locally rigid in the noncompact case.