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

Autor:	Bettiol, Renato G., Lauret, Emilio A., Piccione, Paolo
Rok vydání:	2022
Předmět:	Mathematics - Differential Geometry Mathematics - Spectral Theory Differential Geometry (math.DG) SUPERFÍCIES MÍNIMAS EQUAÇÕES DIFERENCIAIS PARCIAIS General Mathematics FOS: Mathematics Mathematics::Differential Geometry 58J50 53C35 53C30 58J55 53A10 22E46 35J20 Spectral Theory (math.SP)
Zdroj:	Repositório Institucional da USP (Biblioteca Digital da Produção Intelectual) Universidade de São Paulo (USP) instacron:USP
ISSN:	1469-2120 0024-6093
DOI:	10.1112/blms.12650
Popis:	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. LaTeX2e, 19 pages, final (revised) version. To appear in Bull. Lond. Math. Soc
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_dedup___::b826279b0b19b191ec9d6c718b81eab5 https://doi.org/10.1112/blms.12650 Zobrazit plný text záznamu Plný text