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The Resource A theory of branched minimal surfaces, Anthony Tromba
A theory of branched minimal surfaces, Anthony Tromba
Resource Information
The item A theory of branched minimal surfaces, Anthony Tromba represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in Boston University Libraries.This item is available to borrow from all library branches.
Resource Information
The item A theory of branched minimal surfaces, Anthony Tromba represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in Boston University Libraries.
This item is available to borrow from all library branches.
 Summary
 One of the most elementary questions in mathematics is whether an area minimizing surface spanning a contour in three space is immersed or not; i.e. does its derivative have maximal rank everywhere. The purpose of this monograph is to present an elementary proof of this very fundamental and beautiful mathematical result. The exposition follows the original line of attack initiated by Jesse Douglas in his Fields medal work in 1931, namely use Dirichlet's energy as opposed to area. Remarkably, the author shows how to calculate arbitrarily high orders of derivatives of Dirichlet's energy defined on the infinite dimensional manifold of all surfaces spanning a contour, breaking new ground in the Calculus of Variations, where normally only the second derivative or variation is calculated. The monograph begins with easy examples leading to a proof in a large number of cases that can be presented in a graduate course in either manifolds or complex analysis. Thus this monograph requires only the most basic knowledge of analysis, complex analysis and topology and can therefore be read by almost anyone with a basic graduate education
 Language
 eng
 Extent
 1 online resource (ix, 191 pages)
 Contents

 1.Introduction
 2.Higher order Derivatives of Dirichlets' Energy
 3.Very Special Case; The Theorem for n + 1 Even and m + 1 Odd
 4.The First Main Theorem; NonExceptional Branch Points
 5.The Second Main Theorem: Exceptional Branch Points; The Condition k > l
 6.Exceptional Branch Points Without The Condition k > l
 7.New Brief Proofs of the GulliverOssermanRoyden Theorem
 8.Boundary Branch Points
 Scholia
 Appendix
 Bibliography
 Isbn
 9783642256202
 Label
 A theory of branched minimal surfaces
 Title
 A theory of branched minimal surfaces
 Statement of responsibility
 Anthony Tromba
 Subject

 Functions of complex variables
 Global Analysis and Analysis on Manifolds
 Global analysis
 Global differential geometry
 MATHEMATICS  Geometry  Differential
 Mathematical Concepts
 Mathematical Concepts
 Mathematics
 Mathematics
 Mathematics
 Minimal surfaces
 Minimal surfaces
 Minimal surfaces
 Minimal surfaces
 Sequences (Mathematics)
 Sequences, Series, Summability
 Differential Geometry
 Electronic resources
 Functions of a Complex Variable
 Language
 eng
 Summary
 One of the most elementary questions in mathematics is whether an area minimizing surface spanning a contour in three space is immersed or not; i.e. does its derivative have maximal rank everywhere. The purpose of this monograph is to present an elementary proof of this very fundamental and beautiful mathematical result. The exposition follows the original line of attack initiated by Jesse Douglas in his Fields medal work in 1931, namely use Dirichlet's energy as opposed to area. Remarkably, the author shows how to calculate arbitrarily high orders of derivatives of Dirichlet's energy defined on the infinite dimensional manifold of all surfaces spanning a contour, breaking new ground in the Calculus of Variations, where normally only the second derivative or variation is calculated. The monograph begins with easy examples leading to a proof in a large number of cases that can be presented in a graduate course in either manifolds or complex analysis. Thus this monograph requires only the most basic knowledge of analysis, complex analysis and topology and can therefore be read by almost anyone with a basic graduate education
 Cataloging source
 GW5XE
 http://library.link/vocab/creatorName
 Tromba, Anthony
 Image bit depth
 0
 LC call number
 QA644
 LC item number
 .T76 2012
 Literary form
 non fiction
 Nature of contents
 dictionaries
 http://library.link/vocab/relatedWorkOrContributorName
 SpringerLink
 Series statement
 Springer Monographs in Mathematics,
 http://library.link/vocab/subjectName

 Mathematical Concepts
 Mathematics
 Minimal surfaces
 MATHEMATICS
 Minimal surfaces
 Label
 A theory of branched minimal surfaces, Anthony Tromba
 Antecedent source
 mixed
 Bibliography note
 Includes bibliographical references
 Carrier category
 online resource
 Carrier category code

 cr
 Carrier MARC source
 rdacarrier
 Color
 not applicable
 Content category
 text
 Content type code

 txt
 Content type MARC source
 rdacontent
 Contents
 1.Introduction  2.Higher order Derivatives of Dirichlets' Energy  3.Very Special Case; The Theorem for n + 1 Even and m + 1 Odd  4.The First Main Theorem; NonExceptional Branch Points  5.The Second Main Theorem: Exceptional Branch Points; The Condition k > l  6.Exceptional Branch Points Without The Condition k > l  7.New Brief Proofs of the GulliverOssermanRoyden Theorem  8.Boundary Branch Points  Scholia  Appendix  Bibliography
 Dimensions
 unknown
 Extent
 1 online resource (ix, 191 pages)
 File format
 multiple file formats
 Form of item

 online
 electronic
 Isbn
 9783642256202
 Level of compression
 uncompressed
 Media category
 computer
 Media MARC source
 rdamedia
 Media type code

 c
 Other physical details
 portraits.
 Quality assurance targets
 absent
 Reformatting quality
 access
 Specific material designation
 remote
 System control number

 (OCoLC)773291555
 (OCoLC)ocn773291555
 Label
 A theory of branched minimal surfaces, Anthony Tromba
 Antecedent source
 mixed
 Bibliography note
 Includes bibliographical references
 Carrier category
 online resource
 Carrier category code

 cr
 Carrier MARC source
 rdacarrier
 Color
 not applicable
 Content category
 text
 Content type code

 txt
 Content type MARC source
 rdacontent
 Contents
 1.Introduction  2.Higher order Derivatives of Dirichlets' Energy  3.Very Special Case; The Theorem for n + 1 Even and m + 1 Odd  4.The First Main Theorem; NonExceptional Branch Points  5.The Second Main Theorem: Exceptional Branch Points; The Condition k > l  6.Exceptional Branch Points Without The Condition k > l  7.New Brief Proofs of the GulliverOssermanRoyden Theorem  8.Boundary Branch Points  Scholia  Appendix  Bibliography
 Dimensions
 unknown
 Extent
 1 online resource (ix, 191 pages)
 File format
 multiple file formats
 Form of item

 online
 electronic
 Isbn
 9783642256202
 Level of compression
 uncompressed
 Media category
 computer
 Media MARC source
 rdamedia
 Media type code

 c
 Other physical details
 portraits.
 Quality assurance targets
 absent
 Reformatting quality
 access
 Specific material designation
 remote
 System control number

 (OCoLC)773291555
 (OCoLC)ocn773291555
Subject
 Functions of complex variables
 Global Analysis and Analysis on Manifolds
 Global analysis
 Global differential geometry
 MATHEMATICS  Geometry  Differential
 Mathematical Concepts
 Mathematical Concepts
 Mathematics
 Mathematics
 Mathematics
 Minimal surfaces
 Minimal surfaces
 Minimal surfaces
 Minimal surfaces
 Sequences (Mathematics)
 Sequences, Series, Summability
 Differential Geometry
 Electronic resources
 Functions of a Complex Variable
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<div class="citation" vocab="http://schema.org/"><i class="fa faexternallinksquare fafw"></i> Data from <span resource="http://link.bu.edu/portal/AtheoryofbranchedminimalsurfacesAnthony/CeOn568K5tY/" typeof="Book http://bibfra.me/vocab/lite/Item"><span property="name http://bibfra.me/vocab/lite/label"><a href="http://link.bu.edu/portal/AtheoryofbranchedminimalsurfacesAnthony/CeOn568K5tY/">A theory of branched minimal surfaces, Anthony Tromba</a></span>  <span property="potentialAction" typeOf="OrganizeAction"><span property="agent" typeof="LibrarySystem http://library.link/vocab/LibrarySystem" resource="http://link.bu.edu/"><span property="name http://bibfra.me/vocab/lite/label"><a property="url" href="http://link.bu.edu/">Boston University Libraries</a></span></span></span></span></div>