Nonproper Complete Minimal Surfaces Embedded in H2 x R
Nonproper Complete Minimal Surfaces Embedded in H2 x R
复制标题
嵌入 H2 x R 中的非适当完整最小曲面
DOI：
10.1093/imrn/rnu068
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发表时间：
2014
影响因子：
1
通讯作者：
Rodriguez M
中科院分区：
文献类型：
--
作者：
Rodriguez M
完整最小曲面适当嵌入的例子已经被广泛研究，文献中包含了大量的非平凡曲面。在本文中，我们构造了一大类完全极小曲面的例子，这些曲面不一定是固有的，它们通过垂直平移或螺旋运动是不变的。特别地，我们构造了一大族由垂直平移和螺旋运动嵌入的不不变的非固有完全极小盘，其重要性是双重的。它们在等距的商中具有有限的总曲率，从而突出了与嵌入不满足相同性质的最小表面非常不同的行为。他们表明，关于嵌入最小表面的Calabi-Yau猜想是站不住脚的。
Examples of complete minimal surfaces properly embedded inhave been extensively studied and the literature contains a plethora of nontrivial ones. In this paper, we construct a large class of examples of complete minimal surfaces embedded in, not necessarily proper, which are invariant by a vertical translation or by a screw motion. In particular, we construct a large family of nonproper complete minimal disks embedded ininvariant by a vertical translation and a screw motion and whose importance is two-fold. They have finite total curvature in the quotient ofby the isometry, thus highlighting a very different behavior from minimal surfaces embedded insatisfying the same properties. They show that the Calabi–Yau conjectures for embedded minimal surfaces do not hold in.