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Global Analysis of Minimal Surfaces

Global Analysis of Minimal Surfaces

by Ulrich DierkesAnthony Tromba and Stefan Hildebrandt
Paperback
Publication Date: 14/12/2012

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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 Teichmuller theory. Secondly, various index theorems for minimal theorems are derived, and their consequences for the space of solutions to Plateaus problem are discussed. Finally, a topological approach to minimal surfaces via Fredholm vector fields in the spirit of Smale is presented.
ISBN:
9783642265334
9783642265334
Category:
Optimization
Format:
Paperback
Publication Date:
14-12-2012
Language:
English
Publisher:
Springer-Verlag Berlin and Heidelberg GmbH & Co. KG
Country of origin:
Germany
Edition:
2nd Edition
Pages:
537
Dimensions (mm):
235x155x33mm
Weight:
0.84kg

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