On the Problem of Plateau / Subharmonic Functions

  • Authors
  • Tibor Radó

Part of the Ergebnisse der Mathematik und Ihrer Grenƶgebiete book series (MATHE1, volume 2)

Table of contents

  1. Front Matter
    Pages I-XVII
  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
  7. Tibor Radó
    Pages 117-122
  8. Tibor Radó
    Pages 132-141
  9. Back Matter
    Pages 164-166

About this book

Introduction

A convex function f may be called sublinear in the following sense; if a linear function l is ::=: j at the boundary points of an interval, then l:> j in the interior of that interval also. If we replace the terms interval and linear junction by the terms domain and harmonic function, we obtain a statement which expresses the characteristic property of subharmonic functions of two or more variables. This ge­ neralization, formulated and developed by F. RIEsz, immediately at­ tracted the attention of many mathematicians, both on account of its intrinsic interest and on account of the wide range of its applications. If f (z) is an analytic function of the complex variable z = x + i y. then If (z) I is subharmonic. The potential of a negative mass-distribu­ tion is subharmonic. In differential geometry, surfaces of negative curvature and minimal surfaces can be characterized in terms of sub­ harmonic functions. The idea of a subharmonic function leads to significant applications and interpretations in the fields just referred to, and· conversely, every one of these fields is an apparently in­ exhaustible source of new theorems on subharmonic functions, either by analogy or by direct implication.

Keywords

Functions Plateausches Problem Problem of Plateau Subharmonische Funktion function minimum subharmonic function

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-642-65236-3
  • Copyright Information Springer-Verlag Berlin Heidelberg 1971
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-540-05479-5
  • Online ISBN 978-3-642-65236-3
  • About this book