Abstract
We study the existence and uniqueness problem of compact minimal vertical graphs in $\mathbb{H}^{n}\times\mathbb{R}$, $n\geq2$, 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 $\pi/(2n-2)$.
Citation
Aline Mauricio Barbosa. "Compact minimal vertical graphs with non-connected boundary in $\mathbb{H}^{n}\times\mathbb{R}$." Illinois J. Math. 58 (3) 593 - 617, Fall 2014. https://doi.org/10.1215/ijm/1441790379
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