A Survey of Minimal Surfaces

by Osserman, Robert

• ISBN13: 9780486495149
• ISBN10: 0486495140
• Format: Hardcover
• Copyright: 2002-05-01
• Publisher: Dover Publications

Summary

This hardcover edition ofA Survey of Minimal Surfacesis divided into twelve sections discussing parametric surfaces, non-parametric surfaces, surfaces that minimize area, isothermal parameters on surfaces, Bernstein's theorem, minimal surfaces with boundary, the Gauss map of parametric surfaces in E3, non-parametric minimal surfaces in E3, application of parametric surfaces to non-parametric problems, and parametric surfaces in En. For this edition, Robert Osserman, Professor of Mathematics at Stanford University, has substantially expanded his original work, including the uses of minimal surfaces to settle important conjectures in relativity and topology. He also discusses new work on Plateau's problem and on isoperimetric inequalities. With a new appendix, supplementary references and expanded index, this Dover edition offers a clear, modern and comprehensive examination of minimal surfaces, providing serious students with fundamental insights into an increasingly active and important area of mathematics. Corrected and enlarged Dover republication of the work first published in book form by the Van Nostrand Reinhold Company, New York, 1969. Preface to Dover edition. Appendixes. New appendix updating original edition. References. Supplementary references. Expanded indexes.

Table of Contents

Introduction	1	(2)
Parametric surfaces: local theory	3	(12)
Non-parametric surfaces	15	(5)
Surfaces that minimize area	20	(7)
Isothermal parameters	27	(7)
Bernstein's theorem	34	(9)
Parametric surfaces: global theory Generalized minimal surfaces. Complete surfaces	43	(10)
Minimal surfaces with boundary Plateau problem. Dirichlet problem	53	(10)
Parametric surfaces in E3. The Gauss map	63	(12)
Surfaces in E3. Gauss curvature and total curvature	75	(16)
Non-parametric surfaces in E3 Removable singularities. Dirichlet problem	91	(14)
Application of parametric methods to non-parametric problems. Heinz' inequality. Exterior Dirichlet problem	105	(12)
Parametric surfaces in En: generalized Gauss map	117	(12)
Appendix 1. List of theorems	129	(6)
Appendix 2. Generalizations	135	(8)
Appendix 3. Developments in minimal surfaces, 1970-1985	143	(24)
References	167	(12)
Additional References	179	(22)
Author Index	201	(4)
Subject Index	205