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  • Open Daily: 10am - 10pm
    Alley-side Pickup: 10am - 7pm

    3038 Hennepin Ave Minneapolis, MN
    612-822-4611

Open Daily: 10am - 10pm | Alley-side Pickup: 10am - 7pm
3038 Hennepin Ave Minneapolis, MN
612-822-4611
Global Analysis of Minimal Surfaces

Global Analysis of Minimal Surfaces

Dierkes, Ulrich
Hildebrandt, Stefan
Tromba, Anthony

Paperback

Series: Grundlehren Der Mathematischen Wissenschaften, Book 341

CalculusGeneral Mathematics

ISBN10: 3642265332
ISBN13: 9783642265334
Publisher: Springer
Published: Dec 14 2012
Pages: 537
Weight: 1.65
Height: 1.30 Width: 6.10 Depth: 9.00
Language: English
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.

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