As suggested by the title, this book treats the classical theory of minimal surfaces in
Euclidean spaces by complex analytic methods. The connection between these two subjects …

We construct a family of compact free boundary minimal annuli immersed in the unit ball B 3
of R 3, the first such examples other than the critical catenoid. This solves a problem …

Plateau's problem is not a single conjecture or theorem, but rather an abstract framework,
encompassing a number of different problems in several related areas of mathematics. In its …

A minimal surface, like the soap film of Figure 1, has the property that small pieces minimize
area for a given boundary, even though the whole surface may be unstable. At first, there …

Suppose that M is a complete, embedded minimal surface in R 3 with an infinite number of
ends, finite genus, and compact boundary. We prove that the simple limit ends of M have …

In this paper we survey recent developments in the classical theory of minimal surfaces in
Euclidean spaces which have been obtained as applications of both classical and modern …

This paper is the fifth and final in a series on embedded minimal surfaces. Following our
earlier papers on disks, we prove here two main structure theorems for nonsimply connected …

Near the end of his life, Bernhard Riemann made the marvelous discovery of a 1-parameter
family $ R_ {\lambda} $, $\lambda\in (0,\infty) $, of periodic properly embedded minimal …

We study minimal annuli in $\mathbb {S}^{2}\times\mathbb {R} $ of finite type by relating
them to harmonic maps $\mathbb {C}\to\mathbb {S}^{2} $ of finite type. We rephrase an …

In this paper we prove two theorems. The first one is a structure result that describes the
extrinsic geometry of an embedded surface with constant mean curvature (possibly zero) in …