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Minimal Surfaces
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 vers...
| Clasificación: | Libro Electrónico |
|---|---|
| Autores principales: | , , |
| Autor Corporativo: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Berlin, Heidelberg :
Springer Berlin Heidelberg : Imprint: Springer,
2010.
|
| Edición: | 2nd ed. 2010. |
| Colección: | Grundlehren der mathematischen Wissenschaften, A Series of Comprehensive Studies in Mathematics,
339 |
| Temas: | |
| Acceso en línea: | Texto Completo |
MARC
| LEADER | 00000nam a22000005i 4500 | ||
|---|---|---|---|
| 001 | 978-3-642-11698-8 | ||
| 003 | DE-He213 | ||
| 005 | 20220118153124.0 | ||
| 007 | cr nn 008mamaa | ||
| 008 | 100825s2010 gw | s |||| 0|eng d | ||
| 020 | |a 9783642116988 |9 978-3-642-11698-8 | ||
| 024 | 7 | |a 10.1007/978-3-642-11698-8 |2 doi | |
| 050 | 4 | |a QA402.5-402.6 | |
| 050 | 4 | |a QA315-316 | |
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| 100 | 1 | |a Dierkes, Ulrich. |e author. |4 aut |4 http://id.loc.gov/vocabulary/relators/aut | |
| 245 | 1 | 0 | |a Minimal Surfaces |h [electronic resource] / |c by Ulrich Dierkes, Stefan Hildebrandt, Friedrich Sauvigny. |
| 250 | |a 2nd ed. 2010. | ||
| 264 | 1 | |a Berlin, Heidelberg : |b Springer Berlin Heidelberg : |b Imprint: Springer, |c 2010. | |
| 300 | |a XVI, 692 p. 149 illus., 9 illus. in color. |b online resource. | ||
| 336 | |a text |b txt |2 rdacontent | ||
| 337 | |a computer |b c |2 rdamedia | ||
| 338 | |a online resource |b cr |2 rdacarrier | ||
| 347 | |a text file |b PDF |2 rda | ||
| 490 | 1 | |a Grundlehren der mathematischen Wissenschaften, A Series of Comprehensive Studies in Mathematics, |x 2196-9701 ; |v 339 | |
| 505 | 0 | |a to the Geometry of Surfaces and to Minimal Surfaces -- Differential Geometry of Surfaces in Three-Dimensional Euclidean Space -- Minimal Surfaces -- Representation Formulas and Examples of Minimal Surfaces -- Plateau's Problem -- The Plateau Problem and the Partially Free Boundary Problem -- Stable Minimal- and H-Surfaces -- Unstable Minimal Surfaces -- Graphs with Prescribed Mean Curvature -- to the Douglas Problem -- Problems. | |
| 520 | |a 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 Björling´s 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 Plateau´s 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 Nitsche´s uniqueness theorem and Tomi´s finiteness result. In addition, a theory of unstable solutions of Plateau´s problems is developed which is based on Courant´s mountain pass lemma. Furthermore, Dirichlet´s problem for nonparametric H-surfaces is solved, using the solution of Plateau´s problem for H-surfaces and the pertinent estimates. | ||
| 650 | 0 | |a Mathematical optimization. | |
| 650 | 0 | |a Calculus of variations. | |
| 650 | 0 | |a Geometry, Differential. | |
| 650 | 0 | |a Differential equations. | |
| 650 | 0 | |a Functions of complex variables. | |
| 650 | 0 | |a Mathematical physics. | |
| 650 | 1 | 4 | |a Calculus of Variations and Optimization. |
| 650 | 2 | 4 | |a Differential Geometry. |
| 650 | 2 | 4 | |a Differential Equations. |
| 650 | 2 | 4 | |a Functions of a Complex Variable. |
| 650 | 2 | 4 | |a Theoretical, Mathematical and Computational Physics. |
| 700 | 1 | |a Hildebrandt, Stefan. |e author. |4 aut |4 http://id.loc.gov/vocabulary/relators/aut | |
| 700 | 1 | |a Sauvigny, Friedrich. |e author. |4 aut |4 http://id.loc.gov/vocabulary/relators/aut | |
| 710 | 2 | |a SpringerLink (Online service) | |
| 773 | 0 | |t Springer Nature eBook | |
| 776 | 0 | 8 | |i Printed edition: |z 9783642117527 |
| 776 | 0 | 8 | |i Printed edition: |z 9783642116971 |
| 776 | 0 | 8 | |i Printed edition: |z 9783642265273 |
| 830 | 0 | |a Grundlehren der mathematischen Wissenschaften, A Series of Comprehensive Studies in Mathematics, |x 2196-9701 ; |v 339 | |
| 856 | 4 | 0 | |u https://doi.uam.elogim.com/10.1007/978-3-642-11698-8 |z Texto Completo |
| 912 | |a ZDB-2-SMA | ||
| 912 | |a ZDB-2-SXMS | ||
| 950 | |a Mathematics and Statistics (SpringerNature-11649) | ||
| 950 | |a Mathematics and Statistics (R0) (SpringerNature-43713) | ||