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arXiv · 2109.13007

Some Properties of the Intersection of Free Boundary Minimal Hypersurfaces in Euclidean Balls

Ezequiel Barbosa·Alcides de Carvalho·Roney Santos
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Abstract

In this work, we prove that any two free boundary minimal hypersurfaces in the unit Euclidean ball have an intersection point in any half-ball. This is a strong version of the Frankel property proved by A. Fraser and M. Li \cite{FRLI}. As a consequence, we obtain the two-piece property for free boundary minimal hypersurfaces in the unit ball: every equatorial disk divides any compact minimal hypersurface with free boundary in the unit ball in two connected pieces.

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Ezequiel Barbosa, Alcides de Carvalho, Roney Santos. 2021-09-27. Some Properties of the Intersection of Free Boundary Minimal Hypersurfaces in Euclidean Balls. https://arxiv.org/abs/2109.13007

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