Cover; Title Page; Copyright Page; Preface; Contents; Introduction; 1. Parametric surfaces: local theory; 2. Non-parametric surfaces; 3. Surfaces that minimize area; 4. Isothermal parameters; 5. Bernstein's theorem; 6. Parametric surfaces: global theory Generalized minimal surfaces. Complete surfaces; 7. Minimal surfaces with boundary Plateau problem. Dirichlet problem; 8. Parametric surfaces in E3. The Gauss map; 9. Surfaces in E3. Gauss curvature and total curvature; 10. Non-parametric surfaces in E3 Removable singularities. Dirichlet problem. 11. Application of parametric methods to non-parametric problems. Heinz' inequality. Exterior Dirichlet problem12. Parametric surfaces in En : generalized Gauss map; Appendix 1. List of theorems; Appendix 2. Generalizations; Appendix 3. Developments in minimal surfaces, 1970-1985; References; Additional References; Author Index; Subject Index.

Newly updated accessible study covers parametric and non-parametric surfaces, isothermal parameters, Bernstein's theorem, much more, including such recent developments as new work on Plateau's problem and on isoperimetric inequalities. Clear, comprehensive examination provides profound insights into crucial area of pure mathematics. 1986 edition. Index.