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 ...
Read More
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.
Read Less
Add this copy of Minimal Surfaces to cart. $159.29, new condition, Sold by Ingram Customer Returns Center rated 5.0 out of 5 stars, ships from NV, USA, published 2012 by Springer-Verlag Berlin and Heidelberg GmbH & Co. K.
Edition:
2012, Springer-Verlag Berlin and Heidelberg GmbH & Co. K
Edition:
Softcover reprint of hardcover 2nd edition 2010
Publisher:
Springer-Verlag Berlin and Heidelberg GmbH & Co. K
Published:
2012
Language:
English
Alibris ID:
11658691057
Shipping Options:
Standard Shipping: $4.67
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.
Add this copy of Minimal Surfaces (Hb 2010) to cart. $172.02, new condition, Sold by Books International rated 4.0 out of 5 stars, ships from Toronto, ON, CANADA, published 2010 by Springer.
Add this copy of Minimal Surfaces to cart. $173.01, new condition, Sold by GreatBookPrices rated 4.0 out of 5 stars, ships from Columbia, MD, UNITED STATES, published 2010 by Springer.
Choose your shipping method in Checkout. Costs may vary based on destination.
Seller's Description:
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.
Add this copy of Minimal Surfaces to cart. $187.49, new condition, Sold by GreatBookPricesUK5 rated 4.0 out of 5 stars, ships from Castle Donington, DERBYSHIRE, UNITED KINGDOM, published 2010 by Springer.
Choose your shipping method in Checkout. Costs may vary based on destination.
Seller's Description:
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.
Add this copy of Minimal Surfaces to cart. $192.56, new condition, Sold by Media Smart rated 4.0 out of 5 stars, ships from Hawthorne, CA, UNITED STATES, published 2012 by Springer.
Edition:
2012, Springer-Verlag Berlin and Heidelberg GmbH & Co. K
Add this copy of Minimal Surfaces to cart. $209.61, new condition, Sold by Media Smart rated 4.0 out of 5 stars, ships from Hawthorne, CA, UNITED STATES, published 2010 by Springer.
