Full Laplace spectrum of distance spheres in symmetric spaces of rank one. Issue 5 (28th April 2022)

• Record Type: Journal Article
• Authors: Bettiol, Renato G.; Lauret, Emilio A.; Piccione, Paolo
• Is Part Of: Bulletin of the London Mathematical Society. Volume 54:Issue 5(2022)
• Page Start: 1683
• Page End: 1704
• Publication Date: 2022-04-28
• Subjects: Mathematics -- Periodicals; 510
• DOI: 10.1112/blms.12650
• Languages: English
• ISSNs: 0024-6093

Abstract

Abstract: 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 non‐compact) 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, that is, radii where there is bifurcation of embedded constant mean curvature spheres, and show that distance spheres are stable and locally rigid in the non‐compact case.