Global Analysis of Minimal Surfaces Paperback / softback
by Ulrich Dierkes, Stefan Hildebrandt, Anthony Tromba
Part of the Grundlehren der mathematischen Wissenschaften series
Paperback / softback
Description
Many properties of minimal surfaces are of a global nature, and this is already true for the results treated in the first two volumes of the treatise.
Part I of the present book can be viewed as an extension of these results.
For instance, the first two chapters deal with existence, regularity and uniqueness theorems for minimal surfaces with partially free boundaries.
Here one of the main features is the possibility of "edge-crawling" along free parts of the boundary. The third chapter deals with a priori estimates for minimal surfaces in higher dimensions and for minimizers of singular integrals related to the area functional.
In particular, far reaching Bernstein theorems are derived. The second part of the book contains what one might justly call a "global theory of minimal surfaces" as envisioned by Smale.
First, the Douglas problem is treated anew by using Teichmüller theory.
Secondly, various index theorems for minimal theorems are derived, and their consequences for the space of solutions to Plateau´s problem are discussed.
Finally, a topological approach to minimal surfaces via Fredholm vector fields in the spirit of Smale is presented.
Information
-
Item not Available
- Format:Paperback / softback
- Pages:537 pages, 5 Illustrations, color; 41 Illustrations, black and white; XVI, 537 p. 46 illus., 5 illus
- Publisher:Springer-Verlag Berlin and Heidelberg GmbH & Co. K
- Publication Date:14/12/2012
- Category:
- ISBN:9783642265334
Other Formats
- Hardback from £95.55
- PDF from £93.08
Information
-
Item not Available
- Format:Paperback / softback
- Pages:537 pages, 5 Illustrations, color; 41 Illustrations, black and white; XVI, 537 p. 46 illus., 5 illus
- Publisher:Springer-Verlag Berlin and Heidelberg GmbH & Co. K
- Publication Date:14/12/2012
- Category:
- ISBN:9783642265334
