Survey of Minimal Surfaces极小曲面研究

作者简介

　　A Survey of Minimal Surfaces is 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.

书籍目录

Introduction1. Parametric surfaces: local theory2. Non-parametric surfaces3. Surfaces that minimize area4. Isothermal parameters5. Bernstein's theorem6. Parametric surfaces: global theory Generalized minimal surfaces. Complete surfaces7. Minimal surfaces with boundary Plateau problem. Dirichlet problem8. Parametric surfaces in E3. The Gauss map9. Surfaces in E3. Gauss curvature and total curvature10. Non-parametric surfaces in E3 Removable singularities. Dirichlet problem11. Application of parametric methods to non-parametric problems. Heinz' inequality. Exterior Dirichlet problem12. Parametric surfaces in En : generalized Gauss mapAppendix 1. List of theoremsAppendix 2. GeneralizationsAppendix 3. Developments in minimal surfaces, 1970-1985ReferencesAdditional ReferencesAuthor IndexSubject Index

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