Computer Graphics in Minimal Surface Theory
Computer Graphics in Minimal Surface Theory
复制标题
最小曲面理论中的计算机图形学
DOI：
10.1007/978-4-431-55483-7_2
复制
发表时间：
2015
期刊：
影响因子：
--
通讯作者：
Shoichi Fujimori
中科院分区：
文献类型：
--
作者：
Shoichi Fujimori;Samah Gaber Mohamed;and Mason Pember;Selman Akbulut and Kouichi Yasui;Shoichi Fujimori and Toshihiro Shoda;安井弘一;安井弘一;Shoichi Fujimori
本文对极小曲面理论的计算机辅助研究作一综述。世纪后半期，人们研究了有限全曲率完备极小曲面的整体性质。曲面的恰当嵌入性是曲面整体性质中最重要的性质之一。然而，在20世纪80年代早期之前，只有平面和悬链面被认为是适当嵌入的有限全曲率极小曲面。1982年，C.J. Costa发现了一个新的有限全曲率的完备极小曲面的例子。他没有证明它的嵌入性，但它被视为满足所有已知的必要条件的表面被嵌入，和D.霍夫曼和W.米克斯三世后来证明，该表面实际上是嵌入。计算机图形学是证明这一点的一个非常有用的辅助工具。在本文中，我们介绍了这个有趣的故事。
We give a summary of the computer-aided discoveries in minimal surface theory. In the later half of the 20th century, the global properties of complete minimal surfaces of finite total curvature were investigated. Proper embeddedness of a surface is one of the most important properties amongst the global properties. However, before the early 1980s, only the plane and catenoid were known to be properly embedded minimal surfaces of finite total curvature. In 1982, a new example of a complete minimal surface of finite total curvature was found by C.J. Costa. He did not prove its embeddedness, but it was seen to satisfy all known necessary conditions for the surface to be embedded, and D. Hoffman and W. Meeks III later proved that the surface is in fact embedded. Computer graphics was a very useful aid for proving this. In this paper we introduce this interesting story.