Monographs in Mathematics

Minimal Surfaces and Functions of Bounded Variation

Authors: Giusti

Buy this book

eBook $109.00
price for USA in USD (gross)
  • ISBN 978-1-4684-9486-0
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $149.99
price for USA in USD
  • ISBN 978-0-8176-3153-6
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
About this book

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].

Table of contents (17 chapters)

Buy this book

eBook $109.00
price for USA in USD (gross)
  • ISBN 978-1-4684-9486-0
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $149.99
price for USA in USD
  • ISBN 978-0-8176-3153-6
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Loading...

Recommended for you

Loading...

Bibliographic Information

Bibliographic Information
Book Title
Minimal Surfaces and Functions of Bounded Variation
Authors
Series Title
Monographs in Mathematics
Series Volume
80
Copyright
1984
Publisher
Birkhäuser Basel
Copyright Holder
Springer Science+Business Media New York
eBook ISBN
978-1-4684-9486-0
DOI
10.1007/978-1-4684-9486-0
Softcover ISBN
978-0-8176-3153-6
Series ISSN
1017-0480
Edition Number
1
Number of Pages
XII, 240
Topics