This book presents in a systematic and almost self-contained way the striking analogy between classical function theory, in particular the value distribution theory of holomorphic curves in projective space, on the one hand, and important and beautiful properties of the Gauss map of minimal surfaces on the other. Both theories are developed in the text, including many results of recent research. The relations and analogies between them become completely clear. The book is written for interested graduate students and mathematicians, who want to become more familiar with this modern development in the two classical areas of mathematics, as well as those who intend to do further research on minimal surfaces.

A publication of Vieweg+Teubner. The AMS is exclusive distributor in North America. Vieweg+Teubner Publications are available worldwide from the AMS outside of Germany, Switzerland, Austria, and Japan.

Readership

Table of Contents

• The Gauss map of minimal surfaces in $\mathbf{R}^3$
• The derived curves of a holomorphic curve
• The classical defect relations for holomorphic curves
• Modified defect relation for holomorphic curves
• The Gauss map of complete minimal surfaces in $\mathbf{R}^m$
• Bibliography
• Index