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Minimal Surfaces Tapa blanda - 2012
de Ulrich Dierkes; Contribution by Ruben Jakob; Stefan Hildebrandt
Información de la editorial
Descripción de contraportada
Minimal Surfaces is the first volume of a three volume treatise on minimal surfaces (Grundlehren Nr. 339-341). Each volume can be read and studied independently of the others. The central theme is boundary value problems for minimal surfaces. The treatise is a substantially revised and extended version of the monograph Minimal Surfaces I, II (Grundlehren Nr. 295 & 296). The first volume begins with an exposition of basic ideas of the theory of surfaces in three-dimensional Euclidean space, followed by an introduction of minimal surfaces as stationary points of area, or equivalently, as surfaces of zero mean curvature. The final definition of a minimal surface is that of a nonconstant harmonic mapping X: \Omega\to\R^3 which is conformally parametrized on \Omega\subset\R^2 and may have branch points. Thereafter the classical theory of minimal surfaces is surveyed, comprising many examples, a treatment of Bjrlings initial value problem, reflection principles, a formula of the second variation of area, the theorems of Bernstein, Heinz, Osserman, and Fujimoto. The second part of this volume begins with a survey of Plateaus problem and of some of its modifications. One of the main features is a new, completely elementary proof of the fact that area A and Dirichlet integral D have the same infimum in the class C(G) of admissible surfaces spanning a prescribed contour G. This leads to a new, simplified solution of the simultaneous problem of minimizing A and D in C(G), as well as to new proofs of the mapping theorems of Riemann and Korn-Lichtenstein, and to a new solution of the simultaneous Douglas problem for A and D where G consists of several closed components. Then basic facts of stable minimal surfaces are derived; this is done in the context of stable H-surfaces (i.e. of stable surfaces of prescribed mean curvature H), especially of cmc-surfaces (H = const), and leads to curvature estimates for stable, immersed cmc-surfaces and to Nitsches uniqueness theorem andTomis finiteness result. In addition, a theory of unstable solutions of Plateaus problems is developed which is based on Courants mountain pass lemma. Furthermore, Dirichlets problem for nonparametric H-surfaces is solved, using the solution of Plateaus problem for H-surfaces and the pertinent estimates.
Detalles
- Título Minimal Surfaces
- Autor Ulrich Dierkes; Contribution by Ruben Jakob; Stefan Hildebrandt
- Encuadernación Tapa blanda
- Páginas 692
- Volúmenes 1
- Idioma ENG
- Editorial Springer
- Fecha de publicación 2012-12-01
- Ilustrado Sí
- Features Bibliography, Illustrated
- ISBN 9783642265273 / 3642265278
- Peso 2.1 libras (0.95 kg)
- Dimensiones 9 x 6 x 1.4 pulgadas (22.86 x 15.24 x 3.56 cm)
- Dewey Decimal Code 516.362
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Minimal Surfaces (Grundlehren der mathematischen Wissenschaften, 339)
de Dierkes, Ulrich, Hildebrandt, Stefan, Sauvigny, Friedrich
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Minimal Surfaces
de Ruben Jakob
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New. New Book; Fast Shipping from UK; Not signed; Not First Edition; The Minimal Surfaces.
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Minimal Surfaces
de Dierkes, Ulrich (Author)/ Hildebrandt, Stefan (Author)/ Sauvigny, Friedrich (Author)/ Jakob, Ruben (Contributions by)/ Küster, Albrecht (Contributions by)
- Nuevo
- Tapa blanda
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- Paperback
- ISBN 10 / ISBN 13
- 9783642265273 / 3642265278
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- 2
- Librería
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Exeter, Devon, United Kingdom
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EUR 199.46EUR 11.96 enviando a USA
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Descripción:
Springer, 2012. Paperback. New. 2nd reprint edition. 708 pages. 9.00x6.10x1.60 inches.
Precio
EUR 199.46
EUR 11.96
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