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Survey of Minimal Surfaces极小曲面研究

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Survey of Minimal Surfaces极小曲面研究

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定 价：￥339.00

作 者：RobertOsserman 著 著

出 版 社：

出版时间：2004-5-1

I S B N：0486495140

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    内容简介
    　　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.

    作者简介

    目录
    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 problem
    12. 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

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