Embedded Minimal Surfaces of Finite Topology

Abstract

In this paper we prove that a complete, embedded minimal surface M in R 3 with finite topology and compact boundary (possibly empty) is conformally a compact Riemann surface M with boundary punctured in a finite number of interior points and that M can be represented in terms of meromorphic data on its conformal completion M .In particular, we demonstrate that M is a minimal surface of finite type and describe how this property permits a classification of the asymptotic behavior of M .