Riemann minimal surfaces in higher dimensions

Details Riemann minimal surfaces in higher dimensions Riemann minimal surfaces in higher dimensions

2006-03-28

arxiv.org/abs/math/0603662v1

Mathematics

Differential Geometry

Scientific paper

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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