Geometry V: Minimal Surfaces

Robert Osserman (auth.), R. Osserman (eds.)3540605231, 9783540605232

Osserman (Ed.) Geometry V Minimal Surfaces
The theory of minimal surfaces has expanded in many directions over the past decade or two. This volume gathers in one place an overview of some of the most exciting developments, presented by five of the leading contributors to those developments. Hirotaka Fujimoto, who obtained the definitive results on the Gauss map of minimal surfaces, reports on Nevanlinna Theory and Minimal Surfaces. Stefan Hildebrandt provides an up-to-date account of the Plateau problem and related boundary-value problems. David Hoffman and Hermann Karcher describe the wealth of results on embedded minimal surfaces from the past decade, starting with Costa’s surface and the subsequent Hoffman-Meeks examples. Finally, Leon Simon covers the PDE aspect of minimal surfaces, with a survey of known results both in the classical case of surfaces and in the higher dimensional case. The book will be very useful as a reference and research guide to graduate students and researchers in mathematics.

---

Table of contents :
Front Matter….Pages i-ix
Introduction….Pages 1-3
Complete Embedded Minimal Surfaces of Finite Total Curvature….Pages 5-93
Nevanlinna Theory and Minimal Surfaces….Pages 95-151
Boundary Value Problems for Minimal Surfaces….Pages 153-237
The Minimal Surface Equation….Pages 239-266
Back Matter….Pages 267-275