An Alternative for Constant Mean Curvature Hypersurfaces
Abstract
Let M n+1 be a closed manifold of dimension 3 ≤ n + 1 ≤ 7 equipped with a generic Riemannian metric g.Let c be a positive number.We show that, either there exist infinitely many distinct closed hypersurfaces with constant mean curvature equal to c, or there exist infinitely many distinct hypersurfaces with constant mean curvature less than c but enclosing half the volume of M .
Fields of Study & Subjects
Geometric Analysis and Curvature Flows
Advanced Numerical Analysis Techniques
Advanced Differential Geometry Research
Publication details
- Journal / source
- ANNALI SCUOLA NORMALE SUPERIORE - CLASSE DI SCIENZE
- Publisher
- Scuola Normale Superiore - Edizioni della Normale
- Pages
- 11–11
- Publication date
- 25 June 2026
- Language
- EN