# On the asymptotic Plateau problem in ${\widetilde{\mathrm{SL}}_2(\mathbb{R})}$

25 Feb 2020 Castro-Infantes Jesús

We prove some non-existence results for the asymptotic Plateau problem of minimal and area minimizing surfaces in the homogeneous space ${\widetilde{\mathrm{SL}}_2(\mathbb{R})}$ with isometry group of dimension 4, in terms of their asymptotic boundary. Also, we show that a properly immersed minimal surface in ${\widetilde{\mathrm{SL}}_2(\mathbb{R})}$ contained between two bounded entire minimal graphs separated by vertical distance less than a constant have multigraphical ends... (read more)

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