On the Problem of Plateau

  • Authors
  • Tibor Radó

Part of the Ergebnisse der Mathematik und Ihrer Grenƶgebiete book series (volume 2)

Table of contents

  1. Front Matter
    Pages i-vii
  2. Tibor Radó
    Pages 1-1
  3. Tibor Radó
    Pages 2-18
  4. Tibor Radó
    Pages 19-30
  5. Tibor Radó
    Pages 31-49
  6. Tibor Radó
    Pages 49-68

About this book

Introduction

The most immediate one-dimensional variation problem is certainly the problem of determining an arc of curve, bounded by two given and having a smallest possible length. The problem of deter­ points mining and investigating a surface with given boundary and with a smallest possible area might then be considered as the most immediate two-dimensional variation problem. The classical work, concerned with the latter problem, is summed up in a beautiful and enthusiastic manner in DARBOUX'S Theorie generale des surfaces, vol. I, and in the first volume of the collected papers of H. A. SCHWARZ. The purpose of the present report is to give a picture of the progress achieved in this problem during the period beginning with the Thesis of LEBESGUE (1902). Our problem has always been considered as the outstanding example for the application of Analysis and Geometry to each other, and the recent work in the problem will certainly strengthen this opinion. It seems, in particular, that this recent work will be a source of inspiration to the Analyst interested in Calculus of Variations and to the Geometer interested in the theory of the area and in the theory of the conformal maps of general surfaces. These aspects of the subject will be especially emphasized in this report. The report consists of six Chapters. The first three Chapters are important tools or concerned with investigations which yielded either important ideas for the proofs of the existence theorems reviewed in the last three Chapters.

Keywords

Area Calc Minimal surface Volume boundary element method calculus calculus of variations eXist form geometry minimum proof review theorem tool

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-642-99118-9
  • Copyright Information Springer-Verlag GmbH Berlin Heidelberg 1993
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-642-98307-8
  • Online ISBN 978-3-642-99118-9
  • About this book
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