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arXiv · 1303.3089

Compact minimal vertical graphs with non-connected boundary in $\mathbb{H}^n\times\mathbb{R}$

Aline Mauricio Barbosa
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Abstract

We study the existence and uniqueness problem of compact minimal vertical graphs in $\mathbb{H}^n\times\mathbb{R}$, $n\geq 2$, over bounded domains in the slice $\mathbb{H}^n\times\{0\}$, with non-connected boundary having a finite number of $C^0$ hypersufaces homeomorphic to the sphere $\mathbb{S}^{n-1}$, with prescribed bounded continuous boundary data, under hypotheses relating those data and the geometry of the boundary. We show the nonexistence of compact minimal vertical graphs in $\mathbb{H}^n\times\mathbb{R}$ having the boundary in two slices and the height greater than or equal to $\pi/(2n-2)$.

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Aline Mauricio Barbosa. 2013-03-13. Compact minimal vertical graphs with non-connected boundary in $\mathbb{H}^n\times\mathbb{R}$. https://arxiv.org/abs/1303.3089

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