RUI: Finite Type Minimal Surfaces, Analysis and Computation

拟议的研究项目将集中在与有限类型的极小曲面有关的四个领域。第一个领域将涉及计算极小曲面的魏尔斯特拉斯表示中出现的积分周期的算法的开发。这些周期的确定对于确保有限类型极小曲面是明确定义的至关重要。第二个研究领域将是分析欧几里德三维空间中嵌入哪些有限类型的极小曲面。作者已经完成的分析Hoffman-Meek-Costa曲面的工作将被扩展，并且作者和学生研究助理将研究有限类型极小曲面与生成它们的代数曲线之间的关系。第三个研究部分将是提出者的数学包“有限类型”的扩展。这个程序包将有助于有限类型极小曲面的一般研究。最后，拟议项目的一个组成部分将是1993、1994和1995年暑期期间各有一名学生的暑期研究经历。学生研究活动将与该项目的三个研究领域之一直接相关，并将加强古斯塔夫斯数学/计算机科学系的学生研究方案。

The proposed research project will concentrate on four areas relating to minimal surfaces of finite type. The first area will involve the development of algorithms to calculate integral periods that arise in the Weierstrass representation of minimal surfaces. Determination of these periods is critical in insuring that finite type minimal surfaces are well-defined. The second area of study will be to analyze which finite type minimal surfaces are embedded in Euclidean three- space. Work already completed by the proposer in analyzing Hoffman-Meeks-Costa surfaces will be expanded upon and the proposer and student research assistants will study the relationship between finite type minimal surfaces and the algebraic curves that generate them. A third research component will be the expansion of the proposer's Mathematical package "Finite Type." This package will facilitate the general study of finite type minimal surfaces. Finally, an integral part of the proposed project will be summer research experiences for one student during each of the 1993, 1994, and 1995 summer periods. Student research activities will be directly related to one of the three research areas of the project and will strengthen the student research program of the mathematics/computer science department at Gustavus.