Complete embedded minimal surfaces of finite total curvature

Nikolaos Kapouleas
1997 Journal of differential geometry  
A general construction, for complete embedded minimal surfaces of nite total curvature in Euclidean three-space, is carried out. In particular, examples with an arbitrary number of ends are given for the rst time. The construction amounts to desingularizing the circles of intersection of a collection of coaxial catenoids and planes. The desingularization process uses Scherk's singly periodic surfaces for an approximate construction which i s subsequently corrected by singular perturbation methods.
doi:10.4310/jdg/1214460038 fatcat:rcisu3feoncn5p35sd3ism7g4a