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 ...
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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 Bj???rling???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 andTomi???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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Edition:
Softcover reprint of hardcover 2nd edition 2010
Publisher:
Springer-Verlag Berlin and Heidelberg GmbH & Co. K
Published:
2012
Language:
English
Alibris ID:
17917020782
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New. Contains: Illustrations, black & white, Illustrations, color. Grundlehren der mathematischen Wissenschaften . XVI, 692 p. 149 illus., 9 illus. in color. Intended for professional and scholarly audience.
Edition:
Softcover reprint of hardcover 2nd edition 2010
Publisher:
Springer-Verlag Berlin and Heidelberg GmbH & Co. K
Published:
2012
Language:
English
Alibris ID:
11658691057
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Standard Shipping: $4.57
Choose your shipping method in Checkout. Costs may vary based on destination.
Seller's Description:
New. Print on demand Contains: Illustrations, black & white, Illustrations, color. Grundlehren der mathematischen Wissenschaften . XVI, 692 p. 149 illus., 9 illus. in color. Intended for professional and scholarly audience.
Edition:
Softcover reprint of hardcover 2nd edition 2010
Publisher:
Springer-Verlag Berlin and Heidelberg GmbH & Co. K
Published:
2012
Language:
English
Alibris ID:
17383688261
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Standard Shipping: $4.57
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Seller's Description:
New. 692 p. Grundlehren der mathematischen Wissenschaften , 339. 9 Illustrations, color; 140 Illustrations, black and white; XVI, 692 p. 149 illus., 9 illus. in color. Intended for professional and scholarly audience.
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New. Sewn binding. Paper over boards. 692 p. Contains: Illustrations, black & white, Illustrations, color, Tables, black & white, Frontispiece, Figures. Grundlehren Der Mathematischen Wissenschaften, 339. In Stock. 100% Money Back Guarantee. Brand New, Perfect Condition, allow 4-14 business days for standard shipping. To Alaska, Hawaii, U.S. protectorate, P.O. box, and APO/FPO addresses allow 4-28 business days for Standard shipping. No expedited shipping. All orders placed with expedited shipping will be cancelled. Over 3, 000, 000 happy customers.
