Complete Minimal Surfaces in R Sup 3 of Low Total Curvature

摘要

In this paper we wish to determine all the complete minimal surfaces of genus zero and finite total curvature -8 pi in three-dimensional Euclidean space R sup 3 . The surfaces are written down explicitly, using the Weierstrass representation. They are separated into parameter families of surfaces with the same number of ends and the same Gauss map. Pictures of representative members of each type are given. 12 refs., 16 figs., 5 tabs. (ERA citation 13:025662)