Riemann minimal surfaces in higher dimensions

S. Kaabachi; F. Pacard

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Riemann minimal surfaces in higher dimensions

S. Kaabachi·F. Pacard

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Abstract

We prove the existence of a one parameter family of minimal embedded hypersurfaces in $R^{n+1}$, for $n \geq 3$, which generalize the well known 2 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 2-dimensional case, they are not foliated by spheres.

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BibTeX RIS

S. Kaabachi, F. Pacard. 2006-03-28. Riemann minimal surfaces in higher dimensions. https://arxiv.org/abs/math/0603662

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