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Zoll families of minimal hypersurfaces on the compact rank-one symmetric spaces (C...
| Full text | |
| Author(s): |
Bettiol, Renato G.
;
Lauret, Emilio A.
;
Piccione, Paolo
Total Authors: 3
|
| Document type: | Journal article |
| Source: | BULLETIN OF THE LONDON MATHEMATICAL SOCIETY; v. N/A, p. 22-pg., 2022-04-28. |
| 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. (AU) | |
| FAPESP's process: | 19/09045-3 - Geometry and dynamics between São Paulo and New York |
| Grantee: | Paolo Piccione |
| Support Opportunities: | Regular Research Grants |
| FAPESP's process: | 16/23746-6 - Algebraic, topological and analytical techniques in differential geometry and geometric analysis |
| Grantee: | Paolo Piccione |
| Support Opportunities: | Research Projects - Thematic Grants |