Global Analysis of Minimal Surfaces (Grundlehren der mathematischen Wissenschaften, 341)
ISBN-13:
9783642117053
ISBN-10:
3642117058
Edition:
2nd ed. 1992
Author:
Anthony Tromba, Stefan Hildebrandt, Ulrich Dierkes
Publication date:
2010
Publisher:
Springer
Format:
Hardcover
553 pages
Category:
Applied
,
Mathematical Analysis
,
Mathematics
,
Mathematical Physics
,
Physics
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Edition: 2nd ed. 1992; --/No Dust Jacket; First leaf of prelims (half-title, with color frontis on verso) is torn about 10cm from top edge. Otherwise, a very good+ copy: Binding tight and sturdy, text very good, prev owner's name. Very light shelfwear. NOT ex-lib. Due to the size/weight of this book extra charges may apply for international shipping.Ships from Dinkytown in Minneapolis, Minnesota.
Book details
ISBN-13:
9783642117053
ISBN-10:
3642117058
Edition:
2nd ed. 1992
Author:
Anthony Tromba, Stefan Hildebrandt, Ulrich Dierkes
Publication date:
2010
Publisher:
Springer
Format:
Hardcover
553 pages
Category:
Applied
,
Mathematical Analysis
,
Mathematics
,
Mathematical Physics
,
Physics
Summary
Global Analysis of Minimal Surfaces (Grundlehren der mathematischen Wissenschaften, 341) (ISBN-13: 9783642117053 and ISBN-10: 3642117058), written by authors
Anthony Tromba, Stefan Hildebrandt, Ulrich Dierkes, was published by Springer in 2010.
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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.
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