Global Analysis of Minimal Surfaces (Grundlehren der mathematischen Wissenschaften)

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9783642117053: Global Analysis of Minimal Surfaces (Grundlehren der mathematischen Wissenschaften)

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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“The most complete and thorough record of the ongoing efforts to justify Lagrange’s optimism. ... contain a wealth of new material in the form of newly written chapters and sections ... . a compilation of results and proofs from a vast subject. Here were true scholars in the best sense of the word at work, creating their literary lifetime achievements. They wrote with love for detail, clarity and history, which makes them a pleasure to read. ... will become instantaneous classics.” (Matthias Weber, The Mathematical Association of America, June, 2011)

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Descripción Springer, 2010. Hardback. Estado de conservación: NEW. 9783642117053 This listing is a new book, a title currently in-print which we order directly and immediately from the publisher. Nº de ref. de la librería HTANDREE0352839

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Descripción Springer, 2010. Hardcover. Estado de conservación: New. Never used!. Nº de ref. de la librería P113642117058

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Descripción Springer Okt 2010, 2010. Buch. Estado de conservación: Neu. Neuware - 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. Of particular interest are the so-called 'forced Jacobi fields', which play an important role both for the index theorems and for the branch point theory developed in Vol.2 (Nr. 340). 556 pp. Englisch. Nº de ref. de la librería 9783642117053

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Ulrich Dierkes
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Descripción Springer Okt 2010, 2010. Buch. Estado de conservación: Neu. Neuware - 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. Of particular interest are the so-called 'forced Jacobi fields', which play an important role both for the index theorems and for the branch point theory developed in Vol.2 (Nr. 340). 556 pp. Englisch. Nº de ref. de la librería 9783642117053

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Ulrich Dierkes; Stefan Hildebrandt; Anthony Tromba
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Descripción Springer, 2010. Estado de conservación: New. Nº de ref. de la librería L9783642117053

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Ulrich Dierkes; Stefan Hildebrandt; Anthony Tromba
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Descripción Springer, 2010. Hardcover. Estado de conservación: New. book. Nº de ref. de la librería M3642117058

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Ulrich Dierkes, Stefan Hildebrandt, Anthony Tromba
Editorial: Springer-Verlag Berlin and Heidelberg GmbH Co. KG, Germany (2011)
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Descripción Springer-Verlag Berlin and Heidelberg GmbH Co. KG, Germany, 2011. Hardback. Estado de conservación: New. 2nd ed. 1992. Language: English . Brand New Book. 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 Plateau s problem are discussed. Finally, a topological approach to minimal surfaces via Fredholm vector fields in the spirit of Smale is presented. Nº de ref. de la librería LIB9783642117053

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