Minimal Surfaces in the Round Three‐Sphere by Doubling the Equatorial Two‐Sphere, II
Minimal Surfaces in the Round Three‐Sphere by Doubling the Equatorial Two‐Sphere, II
复制标题
通过将赤道二球体加倍得到圆形三球体中的最小曲面，II
DOI：
--
复制
发表时间：
2014
影响因子：
3
通讯作者：
Peter J. McGrath
中科院分区：
文献类型：
--
作者：
N. Kapouleas;Peter J. McGrath
在之前的一篇论文中，我们在圆形三球S31中构建了新的封闭嵌入光滑最小表面，每个表面都类似于赤道两球Seq2的两个平行副本，由小链状桥连接，链状桥集中在两个平行的圆上，或者赤道圆和两极。在这篇续文中，我们推广了这些结构，使链状桥可以沿着任意数量的平行圆集中，并进一步选择在极点包括桥。目前的结构遵循线性化加倍（LD）方法学在前一篇论文中发展。这里构造的LD解可以很容易地修改，用于具有不对称边[15]的旋转对称最小表面的加倍结构。特别是，它们允许我们开发欧几里得三维空间中的链状体、单位球中的临界链状体和平均曲率流的球形收缩体的双重结构。
In a previous paper, new closed embedded smooth minimal surfaces in the round three‐sphere S31 were constructed, each resembling two parallel copies of the equatorial two‐sphere Seq2 joined by small catenoidal bridges, with the catenoidal bridges concentrating along two parallel circles, or the equatorial circle and the poles. In this sequel, we generalize those constructions so that the catenoidal bridges can concentrate along an arbitrary number of parallel circles, with the further option to include bridges at the poles. The current constructions follow the linearized doubling (LD) methodology developed in the previous paper. The LD solutions constructed here can be modified readily for use to doubling constructions of rotationally symmetric minimal surfaces with asymmetric sides [15]. In particular, they allow us to develop doubling constructions for the catenoid in Euclidean three‐space, the critical catenoid in the unit ball, and the spherical shrinker of the mean curvature flow.