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

Research output: Contribution to journal › Article › peer-review

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.

Original language	English
Pages (from-to)	613-637
Number of pages	25
Journal	Journal of the Institute of Mathematics of Jussieu
Volume	6
Issue number	4
DOIs	https://doi.org/10.1017/S1474748007000060
Publication status	Published - 1 Oct 2007
Externally published	Yes

Keywords

Connected sum method
Minimal hypersurface
Riemann minimal surface

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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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AU - Pacard, Frank

PY - 2007/10/1

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N2 - 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.

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

UR - https://www.scopus.com/pages/publications/34247575088

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DO - 10.1017/S1474748007000060

M3 - Article

AN - SCOPUS:34247575088

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VL - 6

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EP - 637

JO - Journal of the Institute of Mathematics of Jussieu

JF - Journal of the Institute of Mathematics of Jussieu

IS - 4

ER -

Riemann minimal surfaces in higher dimensions

Abstract

Keywords

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