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arXiv · 1807.10780

Uniqueness results for free-boundary minimal hypersurfaces in conformally Euclidean balls and annular domains

Ezequiel Barbosa·Edno Pereira·Rosivaldo Antônio Gonçalves
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Abstract

In this paper we prove that a flat free-boundary minimal $n$-disk, $n\geq3$, in the unit Euclidean ball $B^{n+1}$ is the unique compact free boundary minimal hypersurface in the unit Euclidean ball which the squared norm of the second fundamental form is less than either $\frac{n^2}{4}$ or $\frac{(n-2)^2}{4|x|^2}$. Moreover, we prove analogous results for compact free boundary minimal hypersurfaces in annular domains with a conformally Euclidean metric.

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Ezequiel Barbosa, Edno Pereira, Rosivaldo Antônio Gonçalves. 2018-07-27. Uniqueness results for free-boundary minimal hypersurfaces in conformally Euclidean balls and annular domains. https://arxiv.org/abs/1807.10780

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