ESTIMATES FOR THE TRANSFINITE DIAMETER OF A CONTINUUM,

Abstract

Some estimates for the transfinite diameter of a continuum are derived in terms of elementary geometric quantities connected with it. The main intention is methodological. Variational methods are applied, and the corresponding extremum continua are described by a functional differential equation. In all cases the determination of the extremum continuum is based on rather simple geometric arguments. It is intended that the arguments used should indicate more general methods of solution which could be applied in the calculus of variations for conformal mappings. (Author)

Document Details

Document Type
Technical Report
Publication Date
Apr 24, 1964
Accession Number
AD0621352

Entities

People

  • Edgar Reich
  • Menahem Schiffer

Organizations

  • Stanford University

Tags

DTIC Thesaurus Topics

  • Calculus
  • Calculus Of Variations
  • Conformal Mapping
  • Diameters
  • Differential Equations
  • Equations
  • Mathematical Analysis
  • Mathematics
  • Real Variables
  • Variational Methods

Fields of Study

  • Mathematics

Readers

  • Calculus or Mathematical Analysis
  • Theoretical Analysis.