Riemann minimal surfaces in higher dimensions

Saidi Kaabachi; Frank Pacard

doi:10.1017/S1474748007000060

Riemann minimal surfaces in higher dimensions

Saidi Kaabachi
, Frank Pacard

Université Gustave Eiffel

Résultats de recherche: Contribution à un journal › Article › Revue par des pairs

Résumé

We prove the existence of a one parameter family of minimal embedded hypersurfaces in ℝⁿ⁺¹, for n ≥ 3, which generalize the well known two-dimensional 'Riemann minimal surfaces'. The hypersurfaces we obtain are complete, embedded, simply periodic hypersurfaces which have infinitely many parallel hyperplanar ends. By opposition with the two-dimensional case, they are not foliated by spheres.

langue originale	Anglais
Pages (de - à)	613-637
Nombre de pages	25
journal	Journal of the Institute of Mathematics of Jussieu
Volume	6
Numéro de publication	4
Les DOIs	https://doi.org/10.1017/S1474748007000060
état	Publié - 1 oct. 2007
Modification externe	Oui

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10.1017/S1474748007000060

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title = "Riemann minimal surfaces in higher dimensions",

abstract = "We prove the existence of a one parameter family of minimal embedded hypersurfaces in ℝn+1, for n ≥ 3, which generalize the well known two-dimensional 'Riemann minimal surfaces'. The hypersurfaces we obtain are complete, embedded, simply periodic hypersurfaces which have infinitely many parallel hyperplanar ends. By opposition with the two-dimensional case, they are not foliated by spheres.",

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AB - We prove the existence of a one parameter family of minimal embedded hypersurfaces in ℝn+1, for n ≥ 3, which generalize the well known two-dimensional 'Riemann minimal surfaces'. The hypersurfaces we obtain are complete, embedded, simply periodic hypersurfaces which have infinitely many parallel hyperplanar ends. By opposition with the two-dimensional case, they are not foliated by spheres.

KW - Connected sum method

KW - Minimal hypersurface

KW - Riemann minimal surface

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DO - 10.1017/S1474748007000060

M3 - Article

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Riemann minimal surfaces in higher dimensions

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