RUI: Finite Type Minimal Surfaces, Analysis and Computation

拟议的研究项目将集中在四个方面 与有限型极小曲面有关的区域。 第一个领域将涉及发展 算法来计算积分周期中出现的 极小曲面的Weierstrass表示。 确定这些期限对于确保 有限型极小曲面是良好定义的。 第二个研究领域将是分析哪些 有限型极小曲面嵌入在欧几里德三- 空间 提案人在分析中已经完成的工作 Hoffman-Meeks-Costa曲面将得到扩展， 建议者和学生研究助理将研究 有限型极小曲面与 生成它们的代数曲线。 第三个研究组成部分将是扩大 提议者的数学软件包“有限类型”。“这 一个通用的程序包将方便对有限型的研究 最小的表面。 最后，拟议项目的一个组成部分将 暑期研究经验为一个学生在每个 1993年、1994年和1995年夏季。 学生 研究活动将直接关系到一个 项目的三个研究领域，并将加强 数学/计算机科学学生研究计划 在Gustavus。

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.