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Geometry V

Minimal Surfaces

  • Book
  • © 1997

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Editors:
  1. R. Osserman

    1. Mathematical Sciences Research Institute, Berkeley, USA

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Part of the book series: Encyclopaedia of Mathematical Sciences (EMS, volume 90)

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Table of contents (5 chapters)

  1. Front Matter

    Pages i-ix
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  2. Introduction

    • Robert Osserman
    Pages 1-3

  3. Complete Embedded Minimal Surfaces of Finite Total Curvature

    • David Hoffman, Hermann Karcher
    Pages 5-93

  4. Nevanlinna Theory and Minimal Surfaces

    • Hirotaka Fujimoto
    Pages 95-151

  5. Boundary Value Problems for Minimal Surfaces

    • Stefan Hildebrandt
    Pages 153-237

  6. The Minimal Surface Equation

    • Leon Simon
    Pages 239-266

  7. Back Matter

    Pages 267-275
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Keywords

About this book

Few people outside of mathematics are aware of the varieties of mathemat­ ical experience - the degree to which different mathematical subjects have different and distinctive flavors, often attractive to some mathematicians and repellant to others. The particular flavor of the subject of minimal surfaces seems to lie in a combination of the concreteness of the objects being studied, their origin and relation to the physical world, and the way they lie at the intersection of so many different parts of mathematics. In the past fifteen years a new component has been added: the availability of computer graphics to provide illustrations that are both mathematically instructive and esthetically pleas­ ing. During the course of the twentieth century, two major thrusts have played a seminal role in the evolution of minimal surface theory. The first is the work on the Plateau Problem, whose initial phase culminated in the solution for which Jesse Douglas was awarded one of the first two Fields Medals in 1936. (The other Fields Medal that year went to Lars V. Ahlfors for his contributions to complex analysis, including his important new insights in Nevanlinna Theory.) The second was the innovative approach to partial differential equations by Serge Bernstein, which led to the celebrated Bernstein's Theorem, stating that the only solution to the minimal surface equation over the whole plane is the trivial solution: a linear function.

Editors and Affiliations

  • Mathematical Sciences Research Institute, Berkeley, USA

    R. Osserman

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