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...
Đã lưu trong:
| Những tác giả chính: | , , |
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| Định dạng: | Livre numérique |
| Ngôn ngữ: | Anglais |
| Được phát hành: |
Berlin, Heidelberg :
Springer Berlin Heidelberg
[20..].
Cham : Springer Nature |
| Phiên bản: | 2nd ed. 2010. |
| Loạt: | Grundlehren der mathematischen Wissenschaften, A Series of Comprehensive Studies in Mathematics
339 |
| Truy cập trực tuyến: | Accès sur la plateforme de l'éditeur Accès sur la plateforme Istex Accès Université d'Orléans Accès INSA CVL |
| Chú thích: |
Archives Springer e-books (Licence nationale) Archives Springer e-books (Licence nationale) |
| Autres localisations: | Voir dans le Sudoc |
| Edition sous un autre format: | • Minimal surfaces, Ulrich Dierkes, Stefan Hildebrandt, Friedrich Sauvigny, Revised and enlarged 2nd edition, 2010, Heidelberg, Springer, 1 vol. (XV-688 p.), Grundlehren der mathematischen Wissenschaften, 978-3-642-11697-1 • Minimal Surfaces, Texte imprimé, 9783642117527 • Minimal surfaces, Ulrich Dierkes, Stefan Hildebrandt, Friedrich Sauvigny, Revised and enlarged 2nd edition, 2010, Heidelberg, Springer, 1 vol. (XV-688 p.), Grundlehren der mathematischen Wissenschaften, 978-3-642-11697-1 • Minimal Surfaces, Texte imprimé, 9783642265273 |
| Tóm tắt: | 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 |
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| Mô tả sách: | Archives Springer e-books (Licence nationale) Archives Springer e-books (Licence nationale) |
| số ISBN: | 9783642116988 |
| số ISSN: | 2196-9701 |
| Truy cập: | Accès en ligne pour les établissements français bénéficiaires des licences nationales Accès soumis à abonnement pour tout autre établissement Conditions particulières de réutilisation pour les bénéficiaires des licences nationales. https://www.licencesnationales.fr/springer-nature-ebooks-contrat-licence-ln-2017 |