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arXiv · 2108.00441

Uniqueness of free-boundary minimal hypersurfaces in rotational domains

Ezequiel Barbosa·Allan Freitas·Rodrigo Melo·Feliciano Vitório
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Abstract

In this work, we investigate the existence of compact free-boundary minimal hypersurfaces immersed in several domains. Using an original integral identity for compact free-boundary minimal hypersurfaces that are immersed in a domain whose boundary is a regular level set, we study the case where this domain is a quadric or, more generally, a rotational domain. This existence study is done without topological restrictions. We also obtain a new gap theorem for free boundary hypersurfaces immersed in an Euclidean ball and in a rotational ellipsoid.

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Ezequiel Barbosa, Allan Freitas, Rodrigo Melo, Feliciano Vitório. 2021-08-01. Uniqueness of free-boundary minimal hypersurfaces in rotational domains. https://arxiv.org/abs/2108.00441

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