Minimal hypersurfaces in ℝn × Sm
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Jimmy Petean
Abstract
We classify minimal hypersurfaces in ℝn × Sm with n, m ≥ 2 which are invariant by the canonical action of O(n) × O(m). We also construct compact and noncompact examples of invariant hypersurfaces of constant mean curvature. We show that the minimal hypersurfaces and the noncompact constant mean curvature hypersurfaces are all unstable.
Acknowledgements
The authors would like to thank the anonymous referee for a careful reading of the original version of the manuscript and many helpful comments which were used to improve it.
Communicated by: P. Eberlein
Funding: The authors are supported by grant 220074 of Fondo Sectorial de Investigación para la Educación SEP-CONACYT.
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© 2019 Walter de Gruyter GmbH, Berlin/Boston
Articles in the same Issue
- Frontmatter
- Minimal hypersurfaces in ℝn × Sm
- Higher order Dehn functions for horospheres in products of Hadamard spaces
- Unitals with many Baer secants through a fixed point
- Is a complete, reduced set necessarily of constant width?
- Pseudo-embeddings of the (point, k-spaces)-geometry of PG(n, 2) and projective embeddings of DW(2n − 1, 2)
- Classification of 8-dimensional rank two commutative semifields
- On non-Kähler degrees of complex manifolds
- Quantum Kostka and the rank one problem for 𝔰𝔩2m
- The diffeomorphism type of small hyperplane arrangements is combinatorially determined
- Superforms, tropical cohomology, and Poincaré duality
- Eigenvalues of the weighted Laplacian under the extended Ricci flow
Articles in the same Issue
- Frontmatter
- Minimal hypersurfaces in ℝn × Sm
- Higher order Dehn functions for horospheres in products of Hadamard spaces
- Unitals with many Baer secants through a fixed point
- Is a complete, reduced set necessarily of constant width?
- Pseudo-embeddings of the (point, k-spaces)-geometry of PG(n, 2) and projective embeddings of DW(2n − 1, 2)
- Classification of 8-dimensional rank two commutative semifields
- On non-Kähler degrees of complex manifolds
- Quantum Kostka and the rank one problem for 𝔰𝔩2m
- The diffeomorphism type of small hyperplane arrangements is combinatorially determined
- Superforms, tropical cohomology, and Poincaré duality
- Eigenvalues of the weighted Laplacian under the extended Ricci flow
