One-sided complete stable minimal surfaces
One-sided complete stable minimal surfaces
复制标题
DOI：
10.4310/jdg/1175266182
复制
发表时间：
2006-09
影响因子：
2.5
通讯作者：
A. Ros
中科院分区：
文献类型：
--
作者：
A. Ros
我们证明了欧几里得 3 空间中不存在完整的单边稳定极小曲面。我们通过一两个线性独立平移对 R 的商中的最小面积曲面进行分类，并给出非负弯曲环境空间中紧凑双面索引一最小曲面属的尖锐上限。最后，我们根据表面的拓扑结构从下面估计平坦空间中完整的最小表面的指数。
We prove that there are no complete one-sided stable minimal surfaces in the Euclidean 3-space. We classify least area surfaces in the quotient of R by one or two linearly independent translations and we give sharp upper bounds of the genus of compact twosided index one minimal surfaces in non-negatively curved ambient spaces. Finally we estimate from below the index of complete minimal surfaces in flat spaces in terms of the topology of the surface.