Complete Minimal Surfaces of Finite Total Curvature

This monograph contains an exposition of the theory of minimal surfaces in Euclidean space, with an emphasis on complete minimal surfaces of finite total curvature. Our exposition is based upon the philosophy that the study of finite total curvature complete minimal surfaces in R3, in large measure, coincides with the study of meromorphic functions and linear series on compact Riemann sur­ faces. This philosophy is first indicated in the fundamental theorem of Chern and Osserman: A complete...