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100825s2010 gw | s |||| 0|eng d |
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|a 9783642117060
|9 978-3-642-11706-0
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|a 10.1007/978-3-642-11706-0
|2 doi
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|a QA315-316
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|a QA402.3
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|a QA402.5-QA402.6
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|a PBKQ
|2 bicssc
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|a PBU
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|a MAT005000
|2 bisacsh
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|a MAT029020
|2 bisacsh
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|a 515.64
|2 23
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|a Dierkes, Ulrich.
|e author.
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| 245 |
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|a Global Analysis of Minimal Surfaces
|c by Ulrich Dierkes, Stefan Hildebrandt, Anthony J. Tromba.
|h [electronic resource] /
|
| 264 |
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|a Berlin, Heidelberg :
|b Springer Berlin Heidelberg,
|c 2010.
|
| 300 |
# |
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|a XVI, 537 p.
|b online resource.
|
| 336 |
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|a text
|b txt
|2 rdacontent
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|a computer
|b c
|2 rdamedia
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|a online resource
|b cr
|2 rdacarrier
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|a text file
|b PDF
|2 rda
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| 490 |
1 |
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|a Grundlehren der mathematischen Wissenschaften, A Series of Comprehensive Studies in Mathematics,
|v 341
|x 0072-7830 ;
|
| 505 |
0 |
# |
|a Introduction -- Part I. Free Boundaries and Bernstein Theorems -- 1.Minimal Surfaces with Supporting Half-Planes -- 2.Embedded Minimal Surfaces with Partially Free Boundaries -- 3.Bernstein Theorems and Related Results -- Part II. Global Analysis of Minimal Surfaces -- 4.The General Problem of Plateau: Another Approach -- 5.The Index Theorems for Minimal Surfaces of Zero and Higher Genus -- 6.Euler Characteristic and Morse Theory for Minimal Surfaces -- Bibliography -- Index.
|
| 520 |
# |
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|a 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<U+00fc>ller theory. Secondly, various index theorems for minimal theorems are derived, and their consequences for the space of solutions to Plateauþs problem are discussed. Finally, a topological approach to minimal surfaces via Fredholm vector fields in the spirit of Smale is presented.
|
| 650 |
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|a Mathematics.
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| 650 |
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|a Functions of complex variables.
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| 650 |
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|a Global analysis.
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| 650 |
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|a Differential equations, partial.
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| 650 |
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|a Global differential geometry.
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| 650 |
1 |
4 |
|a Mathematics.
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| 650 |
2 |
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|a Calculus of Variations and Optimal Control, Optimization.
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| 650 |
2 |
4 |
|a Differential Geometry.
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| 650 |
2 |
4 |
|a Partial Differential Equations.
|
| 650 |
2 |
4 |
|a Functions of a Complex Variable.
|
| 650 |
2 |
4 |
|a Theoretical, Mathematical and Computational Physics.
|
| 650 |
2 |
4 |
|a Global Analysis and Analysis on Manifolds.
|
| 700 |
1 |
# |
|a Hildebrandt, Stefan.
|e author.
|
| 700 |
1 |
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|a Tromba, Anthony J.
|e author.
|
| 710 |
2 |
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|a SpringerLink (Online service)
|
| 773 |
0 |
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|t Springer eBooks
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| 776 |
0 |
8 |
|i Printed edition:
|z 9783642117053
|
| 830 |
# |
0 |
|a Grundlehren der mathematischen Wissenschaften, A Series of Comprehensive Studies in Mathematics,
|v 341
|x 0072-7830 ;
|
| 856 |
4 |
0 |
|u https://ezaccess.library.uitm.edu.my/login?url=http://dx.doi.org/10.1007/978-3-642-11706-0
|
| 912 |
# |
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|a ZDB-2-SMA
|
| 950 |
# |
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|a Mathematics and Statistics (Springer-11649)
|