Lectures on Minimal Surfaces: Volume 1, Introduction, Fundamentals, Geometry and Basic Boundary Value Problems

This broad 1989 monograph deals with parametric minimal surfaces in Euclidean space.

Johannes C. C. Nitsche (Author)

9780521137782, Cambridge University Press

Paperback, published 3 March 2011

592 pages
22.9 x 15.2 x 3.3 cm, 0.86 kg

Review of the hardback: From a review of the German edition: 'The work in its entirety bespeaks a monumental effort. I was repeatedly astonished by the thoroughness with which the author tracked down references and checked out different treatments of a topic … Nitsche's book will be an invaluable aid to anyone working in the field for years and probably decades to come.' Bulletin of the American Mathematical Society

This 1989 monograph deals with parametric minimal surfaces in Euclidean space. The author presents a broad survey which extends from the classical beginnings to the current situation whilst highlighting many of the subject's main features and interspersing the mathematical development with pertinent historical remarks. The presentation is complete and is complemented by a bibliography of nearly 1600 references. The careful expository style and emphasis on geometric aspects are extremely valuable. Moreover, in the years leading up to the publication of this book, the theory of minimal surfaces was finding increasing application to other areas of mathematics and the physical sciences ensuring that this account will appeal to non-specialists as well.

Preface to the English edition
Preface to the German edition
1. Introduction
2. Curves and Surfaces
3. Conformal mapping and minimal surfaces
4. Results from analysis
5. Plateau's problem
Appendix
References
Name Index
Subject Index.

Subject Areas: Differential & Riemannian geometry [PBMP]