Properly embedded minimal surfaces with finite total curvature
Properly embedded minimal surfaces with finite total curvature
复制标题
正确嵌入具有有限总曲率的最小曲面
DOI：
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发表时间：
2002
期刊：
影响因子：
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通讯作者：
A. Ros
中科院分区：
文献类型：
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作者：
Joaquín Pérez;A. Ros
在欧几里得三空间中正确嵌入的最小曲面中，那些具有来自自然且重要子类的有限总曲率的曲面。除了飞机和 Catenoid 之外，第一个重要的例子是几年前由 Costa [9]、Hoffman 和 Meeks [16]、[17] 构建的。这些例子开始研究有限总曲率最小曲面的存在性、唯一性和结构定理，通常关注它们的拓扑。几种方法竞相解决该理论中的主要问题，尽管到目前为止，这种具有固定拓扑的表面的空间结构还没有得到很好的理解。然而，我们今天处理了一定数量的部分结果，其中一些将在这些注释中进行解释。
Among properly embedded minimal surfaces in Euclidean three space, those that have finite total curvature from a natural and important subclass. The first nontrivial examples, other than the plane and the Catenoid, were constructed only some years ago by Costa [9], and Hoffman and Meeks [16], [17]. These examples began the study of existence, uniqueness and structure theorems for minimal surfaces of finite total curvature, usually attending to their topology. Several methods compete to solve the main problems in this theory, although up to now, the structure of the space of such kind of surfaces with a fixed topology is not well understood. However, we dispose today of a certain number of partial results, and some of them will be explained in these notes.