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 ...
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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 Teichm???ller 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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Seller's Description:
Good. No Dust Jacket. Size: 9x6x1; 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.
Publisher:
Springer-Verlag Berlin and Heidelberg GmbH & Co. K
Published:
2012
Language:
English
Alibris ID:
11658692331
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Seller's Description:
New. 537 p. Grundlehren der mathematischen Wissenschaften , 341. 5 Illustrations, color; 41 Illustrations, black and white; XVI, 537 p. 46 illus., 5 illus. in color. Intended for professional and scholarly audience.
