On the Problem of Plateau

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.

On the Problem of Plateau

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.

More Books:

On the Problem of Plateau
Language: en
Pages: 109
Authors: Tibor Radó
Categories: Mathematics
Type: BOOK - Published: 2013-11-11 - Publisher: Springer

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 Problem of Plateau
Language: en
Pages: 335
Authors: Themistocles M. Rassias
Categories: Mathematics
Type: BOOK - Published: 1992 - Publisher: World Scientific

This volume consists of papers written by eminent scientists from the international mathematical community, who present the latest information concerning the problem of Plateau after its classical solution by Jesse Douglas and Tibor Rad¢. The contributing papers provide insight and perspective on various problems in modern topics of Calculus of
On the Problem of Plateau / Subharmonic Functions
Language: en
Pages: 109
Authors: T. Rado
Categories: Mathematics
Type: BOOK - Published: 1971-01-04 - Publisher: Springer

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
Minimal Surfaces I
Language: en
Pages: 508
Authors: Ulrich Dierkes, Stefan Hildebrandt, Albrecht Küster, Ortwin Wohlrab
Categories: Mathematics
Type: BOOK - Published: 2013-11-27 - Publisher: Springer Science & Business Media

Minimal surfaces I is an introduction to the field of minimal surfaces and apresentation of the classical theory as well as of parts of the modern development centered around boundary value problems. Part II deals with the boundary behaviour of minimal surfaces. Part I is particularly apt for students who
Minimal Surfaces II
Language: en
Pages: 422
Authors: Ulrich Dierkes, Stefan Hildebrandt, Albrecht Küster, Ortwin Wohlrab
Categories: Mathematics
Type: BOOK - Published: 2013-03-14 - Publisher: Springer Science & Business Media

Minimal Surfaces I is an introduction to the field of minimal surfaces and a presentation of the classical theory as well as of parts of the modern development centered around boundary value problems. Part II deals with the boundary behaviour of minimal surfaces. Part I is particularly apt for students