The Resource Constant mean curvature surfaces with boundary, Rafael López, (electronic book)
Constant mean curvature surfaces with boundary, Rafael López, (electronic book)
Resource Information
The item Constant mean curvature surfaces with boundary, Rafael López, (electronic book) represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in University of Liverpool.This item is available to borrow from 1 library branch.
Resource Information
The item Constant mean curvature surfaces with boundary, Rafael López, (electronic book) represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in University of Liverpool.
This item is available to borrow from 1 library branch.
 Summary
 The study of surfaces with constant mean curvature (CMC) is one of the main topics in classical differential geometry. Moreover, CMC surfaces are important mathematical models for the physics of interfaces in the absence of gravity, where they separate two different media, or for capillary phenomena. Further, as most techniques used in the theory of CMC surfaces not only involve geometric methods but also PDE and complex analysis, the theory is also of great interest for many other mathematical fields. While minimal surfaces and CMC surfaces in general have already been treated in the literature, the present work is the first to present a comprehensive study of "compact surfaces with boundaries," narrowing its focus to a geometric view. Basic issues include the discussion whether the symmetries of the curve inherit to the surface; the possible values of the mean curvature, area and volume; stability; the circular boundary case; and the existence of the Plateau problem in the nonparametric case. The exposition provides an outlook on recent research but also a set of techniques that allows the results to be expanded to other ambient spaces. Throughout the text, numerous illustrations clarify the results and their proofs. The book is intended for graduate students and researchers in the field of differential geometry and especially theory of surfaces, including geometric analysis and geometric PDEs. It guides readers up to the stateoftheart of the theory and introduces them to interesting open problems
 Language
 eng
 Extent
 1 online resource (xiv, 292 pages)
 Contents

 Surfaces with Constant Mean Curvature
 Constant Mean Curvature Embedded Surfaces.The Flux Formula for Constant Mean Curvature Surfaces
 The Area and the Volume of a Constant Mean Curvature Surface
 Constant Mean Curvature Discs with Circular Boundary
 The Dirichlet Problem of the CMC Equation
 The Dirichlet Problem in Unbounded Domains
 Constant Mean Curvature Surfaces in Hyperbolic Space
 The Dirichlet Problem in Hyperbolic Space
 Constant Mean Curvature Surfaces in LorentzMinkowski Space
 Appendix: A. The Variation Formula of the Area and the Volume
 B.Open Questions
 Isbn
 9783642396267
 Label
 Constant mean curvature surfaces with boundary
 Title
 Constant mean curvature surfaces with boundary
 Statement of responsibility
 Rafael López
 Language
 eng
 Summary
 The study of surfaces with constant mean curvature (CMC) is one of the main topics in classical differential geometry. Moreover, CMC surfaces are important mathematical models for the physics of interfaces in the absence of gravity, where they separate two different media, or for capillary phenomena. Further, as most techniques used in the theory of CMC surfaces not only involve geometric methods but also PDE and complex analysis, the theory is also of great interest for many other mathematical fields. While minimal surfaces and CMC surfaces in general have already been treated in the literature, the present work is the first to present a comprehensive study of "compact surfaces with boundaries," narrowing its focus to a geometric view. Basic issues include the discussion whether the symmetries of the curve inherit to the surface; the possible values of the mean curvature, area and volume; stability; the circular boundary case; and the existence of the Plateau problem in the nonparametric case. The exposition provides an outlook on recent research but also a set of techniques that allows the results to be expanded to other ambient spaces. Throughout the text, numerous illustrations clarify the results and their proofs. The book is intended for graduate students and researchers in the field of differential geometry and especially theory of surfaces, including geometric analysis and geometric PDEs. It guides readers up to the stateoftheart of the theory and introduces them to interesting open problems
 Cataloging source
 GW5XE
 http://library.link/vocab/creatorName
 López, Rafael
 Dewey number
 516.3/6
 Illustrations
 illustrations
 Index
 index present
 LC call number
 QA645
 Literary form
 non fiction
 Nature of contents

 dictionaries
 bibliography
 Series statement
 Springer monographs in mathematics,
 http://library.link/vocab/subjectName

 Surfaces of constant curvature
 Curves, Algebraic
 Boundary value problems
 Label
 Constant mean curvature surfaces with boundary, Rafael López, (electronic book)
 Antecedent source
 unknown
 Bibliography note
 Includes bibliographical references and index
 Color
 multicolored
 Contents
 Surfaces with Constant Mean Curvature  Constant Mean Curvature Embedded Surfaces.The Flux Formula for Constant Mean Curvature Surfaces  The Area and the Volume of a Constant Mean Curvature Surface  Constant Mean Curvature Discs with Circular Boundary  The Dirichlet Problem of the CMC Equation  The Dirichlet Problem in Unbounded Domains  Constant Mean Curvature Surfaces in Hyperbolic Space  The Dirichlet Problem in Hyperbolic Space  Constant Mean Curvature Surfaces in LorentzMinkowski Space  Appendix: A. The Variation Formula of the Area and the Volume  B.Open Questions
 Control code
 SPR857904343
 Dimensions
 unknown
 Extent
 1 online resource (xiv, 292 pages)
 File format
 unknown
 Form of item
 online
 Isbn
 9783642396267
 Level of compression
 unknown
 Other control number
 10.1007/9783642396267
 Other physical details
 illustrations.
 Quality assurance targets
 not applicable
 Reformatting quality
 unknown
 Reproduction note
 Electronic resource.
 Sound
 unknown sound
 Specific material designation
 remote
 Label
 Constant mean curvature surfaces with boundary, Rafael López, (electronic book)
 Antecedent source
 unknown
 Bibliography note
 Includes bibliographical references and index
 Color
 multicolored
 Contents
 Surfaces with Constant Mean Curvature  Constant Mean Curvature Embedded Surfaces.The Flux Formula for Constant Mean Curvature Surfaces  The Area and the Volume of a Constant Mean Curvature Surface  Constant Mean Curvature Discs with Circular Boundary  The Dirichlet Problem of the CMC Equation  The Dirichlet Problem in Unbounded Domains  Constant Mean Curvature Surfaces in Hyperbolic Space  The Dirichlet Problem in Hyperbolic Space  Constant Mean Curvature Surfaces in LorentzMinkowski Space  Appendix: A. The Variation Formula of the Area and the Volume  B.Open Questions
 Control code
 SPR857904343
 Dimensions
 unknown
 Extent
 1 online resource (xiv, 292 pages)
 File format
 unknown
 Form of item
 online
 Isbn
 9783642396267
 Level of compression
 unknown
 Other control number
 10.1007/9783642396267
 Other physical details
 illustrations.
 Quality assurance targets
 not applicable
 Reformatting quality
 unknown
 Reproduction note
 Electronic resource.
 Sound
 unknown sound
 Specific material designation
 remote
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<div class="citation" vocab="http://schema.org/"><i class="fa faexternallinksquare fafw"></i> Data from <span resource="http://link.liverpool.ac.uk/portal/Constantmeancurvaturesurfaceswithboundary/fg6bsIZFJWE/" typeof="Book http://bibfra.me/vocab/lite/Item"><span property="name http://bibfra.me/vocab/lite/label"><a href="http://link.liverpool.ac.uk/portal/Constantmeancurvaturesurfaceswithboundary/fg6bsIZFJWE/">Constant mean curvature surfaces with boundary, Rafael López, (electronic book)</a></span>  <span property="potentialAction" typeOf="OrganizeAction"><span property="agent" typeof="LibrarySystem http://library.link/vocab/LibrarySystem" resource="http://link.liverpool.ac.uk/"><span property="name http://bibfra.me/vocab/lite/label"><a property="url" href="http://link.liverpool.ac.uk/">University of Liverpool</a></span></span></span></span></div>