RUI: Finite Type Minimal Surfaces, Analysis and Computation

拟议的研究项目将集中在与有限型最小曲面有关的四个领域。第一个领域将涉及算法的发展，以计算在最小曲面的Weierstrass表示中出现的积分周期。这些周期的确定对于保证有限型最小曲面的定义是至关重要的。研究的第二个领域将是分析哪些有限型最小曲面嵌入欧几里得三维空间中。申请人在分析霍夫曼-米克斯-科斯塔曲面方面已经完成的工作将被扩展，申请人和学生研究助理将研究有限型最小曲面与生成它们的代数曲线之间的关系。第三个研究组成部分将是扩展申请人的数学包“有限类型”。这个包将有利于有限型最小曲面的一般研究。最后，拟议项目的一个组成部分将是1993年、1994年和1995年夏季期间各有一名学生的夏季研究经验。学生的研究活动将直接与该项目的三个研究领域之一相关，并将加强古斯塔夫大学数学/计算机科学系的学生研究计划。

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.