Global Analysis of Minimal Surfaces (Paperback, 2nd ed. 1992)

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.

General

Imprint:	Springer-Verlag
Country of origin:	Germany
Series:	Grundlehren der mathematischen Wissenschaften, 341
Release date:	December 2012
First published:	2010
Authors:	Ulrich Dierkes • Stefan Hildebrandt • Anthony Tromba
Dimensions:	235 x 155 x 33mm (L x W x T)
Format:	Paperback
Pages:	537
Edition:	2nd ed. 1992
ISBN-13:	978-3-642-26533-4
Categories:	Books > Science & Mathematics > Mathematics > Numerical analysis Books > Science & Mathematics > Physics > General Books > Science & Mathematics > Mathematics > Calculus & mathematical analysis > Complex analysis Books > Science & Mathematics > Mathematics > Calculus & mathematical analysis > Differential equations Books > Science & Mathematics > Mathematics > Calculus & mathematical analysis > Calculus of variations Books > Science & Mathematics > Mathematics > Geometry > Differential & Riemannian geometry Books > Science & Mathematics > Mathematics > Applied mathematics > General
LSN:	3-642-26533-2
Barcode:	9783642265334

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