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On the asymptotic Plateau problem in \\({\\widetilde{\\mathrm{SL}}_2(\\mathbb{R})}\\)
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Paper
On the asymptotic Plateau problem in \\({\\widetilde{\\mathrm{SL}}_2(\\mathbb{R})}\\)
2021
Overview
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 \\(\\sqrt{1+4\\tau^2}\\pi\\) have multigraphical ends. Finally, we construct simply connected minimal surfaces with finite total curvature which are not graphs and a family of complete embedded minimal surfaces which are non-proper in \\({\\widetilde{\\mathrm{SL}}_2(\\mathbb{R})}\\).
Publisher
Cornell University Library, arXiv.org
Subject
