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.
