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Fall 2014 Compact minimal vertical graphs with non-connected boundary in $\mathbb{H}^{n}\times\mathbb{R}$
Aline Mauricio Barbosa
Illinois J. Math. 58(3): 593-617 (Fall 2014). DOI: 10.1215/ijm/1441790379

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

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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

Information

Received: 8 October 2013; Revised: 20 January 2014; Published: Fall 2014
First available in Project Euclid: 9 September 2015

zbMATH: 1328.53072
MathSciNet: MR3395952
Digital Object Identifier: 10.1215/ijm/1441790379

Subjects:
Primary: 53A10
Secondary: 35J25, 53C42

Rights: Copyright © 2014 University of Illinois at Urbana-Champaign

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Vol.58 • No. 3 • Fall 2014
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