Non-simply connected minimal planar domains in ℍ²×ℝ

Martín, Francisco; Rodríguez, M.

doi:10.1090/S0002-9947-2013-05794-7

Non-simply connected minimal planar domains in $\mathbb {H}^2\times \mathbb {R}$
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by Francisco Martín and M. Magdalena Rodríguez PDF

Trans. Amer. Math. Soc. 365 (2013), 6167-6183 Request permission

Abstract:

We prove that any non-simply connected planar domain can be properly and minimally embedded in $\mathbb {H}^2\times \mathbb {R}$. The examples that we produce are vertical bi-graphs, and they are obtained from the conjugate surface of a Jenkins-Serrin graph.

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