论文标题
在$ {\ widetilde {\ mathrm {sl}} _ 2（\ mathbb {r}）} $中的渐近高原问题上
On the asymptotic Plateau problem in ${\widetilde{\mathrm{SL}}_2(\mathbb{R})}$
论文作者
论文摘要
我们证明了一些不存在的结果，即渐近高原问题的最小和区域最小化表面中的表面$ {\ wideTilde {\ wideRm {\ mathrm {sl}} _ 2（\ \ mathbb {r}）} $ a IDENEMER 4，在其渐近性的边界上，均匀的iSormentry组4。另外，我们表明，适当沉浸的最小表面在$ {\ wideTilde {\ mathrm {sl}} _ 2（\ Mathbb {r}）} $中包含的两个有界的整个最小图之间，由垂直距离隔开，垂直距离小于$ \ sqrt {1+4+4τ2}π$ dield teend undimal deend。最后，我们简单地将最小表面与有限的总曲率连接起来，这不是图形和一个完整的嵌入式最小表面的家族，这些表面是$ {\ widetilde {\ mathrm {sl}}} _ 2（\ mathbb {r}）} $的无孔子。
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 $\sqrt{1+4τ^2}π$ 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 ${\widetilde{\mathrm{SL}}_2(\mathbb{R})}$.
