Minimal Surfaces and Functions of Bounded Variation.

Giusti, Enrico.

ISBN 10: 3764331534 / ISBN 13: 9783764331535

Published by Birkhäuser, Boston, Basel, Stuttgart, 1984

About this Item

24 x 17 cm, hardcover with dust jacket, xii, 240 pages, Text in English, very good/ fine condition, see picture. Monographs in Mathematics, vol. 80. ISBN's 3764331534 & 0817631534. 740g.

Seller Inventory # 81138

Bibliographic Details

• Title: Minimal Surfaces and Functions of Bounded Variation.
• Publisher: Birkhäuser, Boston, Basel, Stuttgart
• Publication Date: 1984
• Language: English
• ISBN 10: 3764331534
• ISBN 13: 9783764331535
• Binding: Hardcover
• Dust Jacket Condition: Dust Jacket Included
• Weight: 740 grams
• Seller catalogs:
  • Wiskunde

About this title

Synopsis

The problem of finding minimal surfaces, i. e. of finding the surface of least area among those bounded by a given curve, was one of the first considered after the foundation of the calculus of variations, and is one which received a satis­ factory solution only in recent years. Called the problem of Plateau, after the blind physicist who did beautiful experiments with soap films and bubbles, it has resisted the efforts of many mathematicians for more than a century. It was only in the thirties that a solution was given to the problem of Plateau in 3-dimensional Euclidean space, with the papers of Douglas [DJ] and Rado [R T1, 2]. The methods of Douglas and Rado were developed and extended in 3-dimensions by several authors, but none of the results was shown to hold even for minimal hypersurfaces in higher dimension, let alone surfaces of higher dimension and codimension. It was not until thirty years later that the problem of Plateau was successfully attacked in its full generality, by several authors using measure-theoretic methods; in particular see De Giorgi [DG1, 2, 4, 5], Reifenberg [RE], Federer and Fleming [FF] and Almgren [AF1, 2]. Federer and Fleming defined a k-dimensional surface in IR" as a k-current, i. e. a continuous linear functional on k-forms. Their method is treated in full detail in the splendid book of Federer [FH 1].