The Resource A theory of branched minimal surfaces, Anthony Tromba

A theory of branched minimal surfaces, Anthony Tromba

Label
A theory of branched minimal surfaces
Title
A theory of branched minimal surfaces
Statement of responsibility
Anthony Tromba
Creator
Contributor
Provider
Subject
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
Member of
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
Instantiates
Publication
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; Non-Exceptional 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 Gulliver-Osserman-Royden 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
Publication
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; Non-Exceptional 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 Gulliver-Osserman-Royden 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

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