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140122  eng 
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a 9783642991189

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1 

a Radó, Tibor

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0 
a On the Problem of Plateau
h Elektronische Ressource
c by Tibor Radó

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a 1st ed. 1993

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a Berlin, Heidelberg
b Springer Berlin Heidelberg
c 1993, 1993

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a VII, 109 p. 2 illus
b online resource

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0 

a I. Curves and surfaces  II. Minimal surfaces in the small  III. Minimal surfaces in the large  IV. The nonparametric problem  V. The problem of Plateau in the parametric form  VI. The simultaneous problem in the parametric form. Generalizations

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a Geometry, Differential

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a Calculus of Variations and Optimization

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a Differential Geometry

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a Mathematical optimization

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a Calculus of variations

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0 
7 
a eng
2 ISO 6392

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b SBA
a Springer Book Archives 2004

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a Ergebnisse der Mathematik und ihrer Grenzgebiete. 2. Folge, A Series of Modern Surveys in Mathematics

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a 10.1007/9783642991189

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u https://doi.org/10.1007/9783642991189?nosfx=y
x Verlag
3 Volltext

082 
0 

a 515.64

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a 519.6

520 


a The most immediate onedimensional 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 twodimensional 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
