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
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The item Minimal surfaces, Ulrich Dierkes, Stefan Hildebrandt, Friedrich Sauvigny ; with assistance and contributions by A. Küster and R. Jakob represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in University of Missouri Libraries.This item is available to borrow from 1 library branch.
Resource Information
The item Minimal surfaces, Ulrich Dierkes, Stefan Hildebrandt, Friedrich Sauvigny ; with assistance and contributions by A. Küster and R. Jakob represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in University of Missouri Libraries.
This item is available to borrow from 1 library branch.
 Summary
 Minimal Surfaces is the first volume of a three volume treatise on minimal surfaces (Grundlehren Nr. 339341). 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 threedimensional 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 KornLichtenstein, 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 Hsurfaces (i.e. of stable surfaces of prescribed mean curvature H), especially of cmcsurfaces (H = const), and leads to curvature estimates for stable, immersed cmcsurfaces 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 Hsurfaces is solved, using the solution of Plateau?þs problem for Hsurfaces and the pertinent estimates
 Language
 eng
 Edition
 Rev. and enl. 2nd ed.
 Extent
 1 online resource (xv, 688 pages)
 Contents

 Minimal surfaces
 Regularity of minimal surfaces
 Global theory of mininal surfaces
 Isbn
 9783642116995
 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
 Language
 eng
 Summary
 Minimal Surfaces is the first volume of a three volume treatise on minimal surfaces (Grundlehren Nr. 339341). 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 threedimensional 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 KornLichtenstein, 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 Hsurfaces (i.e. of stable surfaces of prescribed mean curvature H), especially of cmcsurfaces (H = const), and leads to curvature estimates for stable, immersed cmcsurfaces 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 Hsurfaces is solved, using the solution of Plateau?þs problem for Hsurfaces and the pertinent estimates
 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
 339341
 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
 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
 9783642116971
 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
 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
 9783642116971
 Specific material designation
 remote
 System control number
 (OCoLC)668095832
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<div class="citation" vocab="http://schema.org/"><i class="fa faexternallinksquare fafw"></i> Data from <span resource="http://link.library.missouri.edu/portal/MinimalsurfacesUlrichDierkesStefan/hqf2BX5W8ZY/" typeof="Book http://bibfra.me/vocab/lite/Item"><span property="name http://bibfra.me/vocab/lite/label"><a href="http://link.library.missouri.edu/portal/MinimalsurfacesUlrichDierkesStefan/hqf2BX5W8ZY/">Minimal surfaces, Ulrich Dierkes, Stefan Hildebrandt, Friedrich Sauvigny ; with assistance and contributions by A. Küster and R. Jakob</a></span>  <span property="potentialAction" typeOf="OrganizeAction"><span property="agent" typeof="LibrarySystem http://library.link/vocab/LibrarySystem" resource="http://link.library.missouri.edu/"><span property="name http://bibfra.me/vocab/lite/label"><a property="url" href="http://link.library.missouri.edu/">University of Missouri Libraries</a></span></span></span></span></div>