Minimal Surfaces and Functions of Bounded Variation

Minimal Surfaces and Functions of Bounded Variation
Author :
Publisher : Springer Science & Business Media
Total Pages : 250
Release :
ISBN-10 : 9781468494860
ISBN-13 : 1468494864
Rating : 4/5 (864 Downloads)

Book Synopsis Minimal Surfaces and Functions of Bounded Variation by : Giusti

Download or read book Minimal Surfaces and Functions of Bounded Variation written by Giusti and published by Springer Science & Business Media. This book was released on 2013-03-14 with total page 250 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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].


Minimal Surfaces and Functions of Bounded Variation Related Books

Minimal Surfaces and Functions of Bounded Variation
Language: en
Pages: 250
Authors: Giusti
Categories: Mathematics
Type: BOOK - Published: 2013-03-14 - Publisher: Springer Science & Business Media

DOWNLOAD EBOOK

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
Minimal Surfaces and Functions of Bounded Variation
Language: en
Pages: 0
Authors: E. Giusti
Categories:
Type: BOOK - Published: 1977 - Publisher:

DOWNLOAD EBOOK

Boundary Value Problems of Mathematical Physics
Language: en
Pages: 408
Authors: Ivar Stakgold
Categories:
Type: BOOK - Published: 2000 - Publisher:

DOWNLOAD EBOOK

Functions of Bounded Variation and Their Fourier Transforms
Language: en
Pages: 224
Authors: Elijah Liflyand
Categories: Mathematics
Type: BOOK - Published: 2019-03-06 - Publisher: Springer

DOWNLOAD EBOOK

Functions of bounded variation represent an important class of functions. Studying their Fourier transforms is a valuable means of revealing their analytic prop
Minimal Surfaces II
Language: en
Pages: 435
Authors: Ulrich Dierkes
Categories: Mathematics
Type: BOOK - Published: 2013-03-14 - Publisher: Springer Science & Business Media

DOWNLOAD EBOOK

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