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

Autor(es)

Bettiol, Renato G. ; Lauret, Emilio A. ; Piccione, Paolo

• Tipo de documento: Artigo Científico
• Fonte: BULLETIN OF THE LONDON MATHEMATICAL SOCIETY; v. N/A, p. 22-pg., 2022-04-28.

Resumo

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. (AU)

• Processo FAPESP: 19/09045-3 - Geometria e dinâmica entre São Paulo e Nova Iorque
• Beneficiário: Paolo Piccione
• Modalidade de apoio: Auxílio à Pesquisa - Regular
• Processo FAPESP: 16/23746-6 - Técnicas algébricas, topológicas e analíticas em geometria diferencial e análise geométrica
• Beneficiário: Paolo Piccione
• Modalidade de apoio: Auxílio à Pesquisa - Temático