Coverart for item
The Resource Minimal surfaces, Ulrich Dierkes, Stefan Hildebrandt, Friedrich Sauvigny ; with assistance and contributions by A. Küster and R. Jakob

Minimal surfaces, Ulrich Dierkes, Stefan Hildebrandt, Friedrich Sauvigny ; with assistance and contributions by A. Küster and R. Jakob

Label
Minimal surfaces
Title
Minimal surfaces
Statement of responsibility
Ulrich Dierkes, Stefan Hildebrandt, Friedrich Sauvigny ; with assistance and contributions by A. Küster and R. Jakob
Creator
Contributor
Subject
Language
eng
Summary
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\R3̂ which is conformally parametrized on \Omega\subset\R2̂ and may have branch points. Thereafter the classical theory of minimal surfaces is surveyed, comprising many examples, a treatment of Bj?œrling?þs 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?þs 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?þs uniqueness theorem and Tomi?þs finiteness result. In addition, a theory of unstable solutions of Plateau?þs problems is developed which is based on Courant?þs mountain pass lemma. Furthermore, Dirichlet?þs problem for nonparametric H-surfaces is solved, using the solution of Plateau?þs problem for H-surfaces and the pertinent estimates
Member of
Cataloging source
GW5XE
http://library.link/vocab/creatorName
Dierkes, Ulrich
Dewey number
516.362
Illustrations
illustrations
Index
index present
LC call number
QA644
LC item number
.D54 2010
Literary form
non fiction
Nature of contents
  • dictionaries
  • bibliography
http://library.link/vocab/relatedWorkOrContributorName
  • Hildebrandt, Stefan
  • Sauvigny, Friedrich
  • Jakob, Ruben
  • Küster, Albrecht
  • Dierkes, Ulrich
  • Dierkes, Ulrich
  • Dierkes, Ulrich
Series statement
Grundlehren der mathematischen Wissenschaften,
Series volume
339-341
http://library.link/vocab/subjectName
  • Minimal surfaces
  • Boundary value problems
  • MATHEMATICS
  • Boundary value problems
  • Minimal surfaces
  • Differentialgeometri
Label
Minimal surfaces, Ulrich Dierkes, Stefan Hildebrandt, Friedrich Sauvigny ; with assistance and contributions by A. Küster and R. Jakob
Instantiates
Publication
Bibliography note
Includes bibliographical references and index
Carrier category
online resource
Carrier category code
  • cr
Carrier MARC source
rdacarrier
Color
multicolored
Content category
text
Content type code
  • txt
Content type MARC source
rdacontent
Contents
Minimal surfaces -- Regularity of minimal surfaces -- Global theory of mininal surfaces
Control code
668095832
Dimensions
unknown
Edition
Rev. and enl. 2nd ed.
Extent
1 online resource (xv, 688 pages)
Form of item
online
Isbn
9783642116995
Lccn
2010930922
Media category
computer
Media MARC source
rdamedia
Media type code
  • c
Other physical details
illustrations (some color).
http://library.link/vocab/ext/overdrive/overdriveId
978-3-642-11697-1
Specific material designation
remote
System control number
(OCoLC)668095832
Label
Minimal surfaces, Ulrich Dierkes, Stefan Hildebrandt, Friedrich Sauvigny ; with assistance and contributions by A. Küster and R. Jakob
Publication
Bibliography note
Includes bibliographical references and index
Carrier category
online resource
Carrier category code
  • cr
Carrier MARC source
rdacarrier
Color
multicolored
Content category
text
Content type code
  • txt
Content type MARC source
rdacontent
Contents
Minimal surfaces -- Regularity of minimal surfaces -- Global theory of mininal surfaces
Control code
668095832
Dimensions
unknown
Edition
Rev. and enl. 2nd ed.
Extent
1 online resource (xv, 688 pages)
Form of item
online
Isbn
9783642116995
Lccn
2010930922
Media category
computer
Media MARC source
rdamedia
Media type code
  • c
Other physical details
illustrations (some color).
http://library.link/vocab/ext/overdrive/overdriveId
978-3-642-11697-1
Specific material designation
remote
System control number
(OCoLC)668095832

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