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Minimal Surfaces (Record no. 192239)

MARC details
000 -LEADER
fixed length control field	04984nam a22006015i 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	20160302165849.0
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 - PRODUCTION, PUBLICATION, DISTRIBUTION, MANUFACTURE, AND COPYRIGHT NOTICE
Place of production, publication, distribution, manufacture	Berlin, Heidelberg :
Name of producer, publisher, distributor, manufacturer	Springer Berlin Heidelberg,
Date of production, publication, distribution, manufacture, or copyright notice	2010.
300 ## - PHYSICAL DESCRIPTION
Extent	XVI, 692 p. 149 illus., 9 illus. in color.
Other physical details	online resource.
336 ## - CONTENT TYPE
Content type term	text
Content type code	txt
Source	rdacontent
337 ## - MEDIA TYPE
Media type term	computer
Media type code	c
Source	rdamedia
338 ## - CARRIER TYPE
Carrier type term	online resource
Carrier type code	cr
Source	rdacarrier
347 ## - DIGITAL FILE CHARACTERISTICS
File type	text file
Encoding format	PDF
Source	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/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 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 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	Partial differential equations.
650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM
Topical term or geographic name as entry element	Differential geometry.
650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM
Topical term or geographic name as entry element	Calculus of variations.
650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM
Topical term or geographic name as entry element	Physics.
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
Relationship information	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,
International Standard Serial Number	0072-7830 ;
Volume number/sequential designation	339
856 40 - ELECTRONIC LOCATION AND ACCESS
Uniform Resource Identifier	<a href="http://dx.doi.org/10.1007/978-3-642-11698-8">http://dx.doi.org/10.1007/978-3-642-11698-8</a>
912 ## -
--	ZDB-2-SMA

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