Minimal Surfaces (Record no. 111915)
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000 -LEADER | |
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fixed length control field | 04883nam a22005775i 4500 |
001 - CONTROL NUMBER | |
control field | 978-3-642-11698-8 |
003 - CONTROL NUMBER IDENTIFIER | |
control field | DE-He213 |
005 - DATE AND TIME OF LATEST TRANSACTION | |
control field | 20140220084531.0 |
007 - PHYSICAL DESCRIPTION FIXED FIELD--GENERAL INFORMATION | |
fixed length control field | cr nn 008mamaa |
008 - FIXED-LENGTH DATA ELEMENTS--GENERAL INFORMATION | |
fixed length control field | 100825s2010 gw | s |||| 0|eng d |
020 ## - INTERNATIONAL STANDARD BOOK NUMBER | |
International Standard Book Number | 9783642116988 |
-- | 978-3-642-11698-8 |
024 7# - OTHER STANDARD IDENTIFIER | |
Standard number or code | 10.1007/978-3-642-11698-8 |
Source of number or code | doi |
050 #4 - LIBRARY OF CONGRESS CALL NUMBER | |
Classification number | QA315-316 |
050 #4 - LIBRARY OF CONGRESS CALL NUMBER | |
Classification number | QA402.3 |
050 #4 - LIBRARY OF CONGRESS CALL NUMBER | |
Classification number | QA402.5-QA402.6 |
072 #7 - SUBJECT CATEGORY CODE | |
Subject category code | PBKQ |
Source | bicssc |
072 #7 - SUBJECT CATEGORY CODE | |
Subject category code | PBU |
Source | bicssc |
072 #7 - SUBJECT CATEGORY CODE | |
Subject category code | MAT005000 |
Source | bisacsh |
072 #7 - SUBJECT CATEGORY CODE | |
Subject category code | MAT029020 |
Source | bisacsh |
082 04 - DEWEY DECIMAL CLASSIFICATION NUMBER | |
Classification number | 515.64 |
Edition number | 23 |
100 1# - MAIN ENTRY--PERSONAL NAME | |
Personal name | Dierkes, Ulrich. |
Relator term | author. |
245 10 - TITLE STATEMENT | |
Title | Minimal Surfaces |
Medium | [electronic resource] / |
Statement of responsibility, etc | by Ulrich Dierkes, Stefan Hildebrandt, Friedrich Sauvigny. |
264 #1 - | |
-- | Berlin, Heidelberg : |
-- | Springer Berlin Heidelberg, |
-- | 2010. |
300 ## - PHYSICAL DESCRIPTION | |
Extent | XVI, 692 p. |
Other physical details | online resource. |
336 ## - | |
-- | text |
-- | txt |
-- | rdacontent |
337 ## - | |
-- | computer |
-- | c |
-- | rdamedia |
338 ## - | |
-- | online resource |
-- | cr |
-- | rdacarrier |
347 ## - | |
-- | text file |
-- | |
-- | rda |
490 1# - SERIES STATEMENT | |
Series statement | Grundlehren der mathematischen Wissenschaften, A Series of Comprehensive Studies in Mathematics, |
International Standard Serial Number | 0072-7830 ; |
Volume number/sequential designation | 339 |
505 0# - FORMATTED CONTENTS NOTE | |
Formatted contents note | 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 ## - SUMMARY, ETC. | |
Summary, etc | 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 - SUBJECT ADDED ENTRY--TOPICAL TERM | |
Topical term or geographic name as entry element | Mathematics. |
650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM | |
Topical term or geographic name as entry element | Functions of complex variables. |
650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM | |
Topical term or geographic name as entry element | Differential equations, partial. |
650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM | |
Topical term or geographic name as entry element | Global differential geometry. |
650 14 - SUBJECT ADDED ENTRY--TOPICAL TERM | |
Topical term or geographic name as entry element | Mathematics. |
650 24 - SUBJECT ADDED ENTRY--TOPICAL TERM | |
Topical term or geographic name as entry element | Calculus of Variations and Optimal Control, Optimization. |
650 24 - SUBJECT ADDED ENTRY--TOPICAL TERM | |
Topical term or geographic name as entry element | Differential Geometry. |
650 24 - SUBJECT ADDED ENTRY--TOPICAL TERM | |
Topical term or geographic name as entry element | Partial Differential Equations. |
650 24 - SUBJECT ADDED ENTRY--TOPICAL TERM | |
Topical term or geographic name as entry element | Functions of a Complex Variable. |
650 24 - SUBJECT ADDED ENTRY--TOPICAL TERM | |
Topical term or geographic name as entry element | Theoretical, Mathematical and Computational Physics. |
700 1# - ADDED ENTRY--PERSONAL NAME | |
Personal name | Hildebrandt, Stefan. |
Relator term | author. |
700 1# - ADDED ENTRY--PERSONAL NAME | |
Personal name | Sauvigny, Friedrich. |
Relator term | author. |
710 2# - ADDED ENTRY--CORPORATE NAME | |
Corporate name or jurisdiction name as entry element | SpringerLink (Online service) |
773 0# - HOST ITEM ENTRY | |
Title | Springer eBooks |
776 08 - ADDITIONAL PHYSICAL FORM ENTRY | |
Display text | Printed edition: |
International Standard Book Number | 9783642116971 |
830 #0 - SERIES ADDED ENTRY--UNIFORM TITLE | |
Uniform title | Grundlehren der mathematischen Wissenschaften, A Series of Comprehensive Studies in Mathematics, |
-- | 0072-7830 ; |
Volume number/sequential designation | 339 |
856 40 - ELECTRONIC LOCATION AND ACCESS | |
Uniform Resource Identifier | http://dx.doi.org/10.1007/978-3-642-11698-8 |
912 ## - | |
-- | ZDB-2-SMA |
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