论文标题
$ \ mathrm {nil} _3 $和$ \ widetilde {sl_2}（\ Mathbb {r}）$ \ mathrm {nil} _3 $和$ \ mathrm {nil} _3 $中的规定平均曲率表面
Delaunay surfaces of prescribed mean curvature in $\mathrm{Nil}_3$ and $\widetilde{SL_2}(\mathbb{R})$
论文作者
论文摘要
我们获得了海森堡空间中旋转表面和特殊线性组的通用盖的分类结果，其平均曲率根据其角度函数给出了规定的$ c^1 $函数。我们表明，这些表面的表现就像在规定函数的某些假设下，这些表面的表现就像恒定平均曲率的delaunay表面一样。与恒定的平均曲率情况相反，我们表现出旋转的嵌入式托里的存在，为这类浸泡表面提供了Alexandrov问题的反例。
We obtain a classification result for rotational surfaces in the Heisenberg space and the universal cover of the special linear group, whose mean curvature is given as a prescribed $C^1$ function depending on their angle function. We show that these surfaces behave like the Delaunay surfaces of constant mean curvature, under some assumptions on the prescribed function. In contrast with the constant mean curvature case, we exhibit the existence of rotational, embedded tori, providing counterexamples of the Alexandrov problem for this class of immersed surfaces.
