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arXiv · 2110.01139

A two-piece property for free boundary minimal hypersurfaces in the $(n+1)$-dimensional ball

Vanderson Lima·Ana Menezes
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Abstract

We prove that every hyperplane passing through the origin in $\rr^{n+1}$ divides an embedded compact free boundary minimal hypersurface of the euclidean $(n+1)$-ball in exactly two connected hypersurfaces. We also show that if a region in the $(n+1)$-ball has mean convex boundary and contains a nullhomologous $(n-1)$-dimensional equatorial disk, then this region is a closed halfball. Our first result gives evidence to a conjecture by Fraser and Li in any dimension.

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Vanderson Lima, Ana Menezes. 2021-10-04. A two-piece property for free boundary minimal hypersurfaces in the $(n+1)$-dimensional ball. https://arxiv.org/abs/2110.01139

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