Minimal surfaces in R3 / J. Lucas M. Barbosa, A. Gervasio Colares

The authors give a detailed description of a number of complete minimal surfaces in R3, both classical and more recently discovered surfaces. After a discussion of the elementary theory of minimal surfaces in R3, in particular the Weierstrass representation, the authors describe in detail classical minimal surfaces in R3 including the catenoid, Enneper's surface and Scherk's surface. After this, attention is focussed on more recent constructions of complete minimal surfaces in R3 with small total curvature, small genus and one, two or three ends. For example, there is a discussion of Costa's example, which has since been further analysed by Meeks and Hoffman, and the example of Jorge-Xavier of a complete minimal surface in R3 between parallel planes.
As the authors state in the introduction, this book is not meant to be a full introduction to the study of minimal surfaces in R3. Instead, it illuminates this theory by detailed discussion of many examples. (MathSciNet)