An inverse problem of the flux for minimal surfaces
An inverse problem of the flux for minimal surfaces
复制标题
最小曲面的通量反问题
DOI：
10.1512/iumj.1997.46.960
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发表时间：
1997
期刊：
影响因子：
--
通讯作者：
Kotaro Yamada
中科院分区：
文献类型：
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作者：
S. Kato;M. Umehara;Kotaro Yamada
对于欧氏三维空间中的完备极小曲面，所谓的通量向量对应于每一端。通量矢量是平衡的，即，所有端点的和为零。考虑以下逆问题：对于每个平衡的n个向量，找到一个n端悬链面，该悬链面获得给定的向量作为通量。这里，n端悬链面是亏格为0的完全极小曲面，其端点渐近于悬链面。本文将问题归结为求解代数方程组。使用这种减少，它表明，当n=4，4端悬链的反问题有几乎所有的平衡4向量的解决方案。进一步的障碍物的n端悬链线与平行通量矢量进行了讨论。
For a complete minimal surface in the Euclidean 3-space, the so-called flux vector corresponds to each end. The flux vectors are balanced, i.e., the sum of those over all ends are zero. Consider the following inverse problem: For each balanced n vectors, find an n-end catenoid which attains given vectors as flux. Here, an n-end catenoid is a complete minimal surface of genus 0 with ends asymptotic to the catenoids. In this paper, the problem is reduced to solving algebraic equation. Using this reduction, it is shown that, when n=4, the inverse problem for 4-end catenoid has solutions for almost all balanced 4 vectors. Further obstructions for n-end catenoids with parallel flux vectors are also discussed.