A Theory of Branched Minimal Surfaces (Record no. 102453)
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| 000 -LEADER | |
|---|---|
| fixed length control field | 03310nam a22005055i 4500 |
| 001 - CONTROL NUMBER | |
| control field | 978-3-642-25620-2 |
| 003 - CONTROL NUMBER IDENTIFIER | |
| control field | DE-He213 |
| 005 - DATE AND TIME OF LATEST TRANSACTION | |
| control field | 20140220083306.0 |
| 007 - PHYSICAL DESCRIPTION FIXED FIELD--GENERAL INFORMATION | |
| fixed length control field | cr nn 008mamaa |
| 008 - FIXED-LENGTH DATA ELEMENTS--GENERAL INFORMATION | |
| fixed length control field | 120104s2012 gw | s |||| 0|eng d |
| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER | |
| International Standard Book Number | 9783642256202 |
| -- | 978-3-642-25620-2 |
| 024 7# - OTHER STANDARD IDENTIFIER | |
| Standard number or code | 10.1007/978-3-642-25620-2 |
| Source of number or code | doi |
| 050 #4 - LIBRARY OF CONGRESS CALL NUMBER | |
| Classification number | QA331-355 |
| 072 #7 - SUBJECT CATEGORY CODE | |
| Subject category code | PBKD |
| Source | bicssc |
| 072 #7 - SUBJECT CATEGORY CODE | |
| Subject category code | MAT034000 |
| Source | bisacsh |
| 082 04 - DEWEY DECIMAL CLASSIFICATION NUMBER | |
| Classification number | 515.9 |
| Edition number | 23 |
| 100 1# - MAIN ENTRY--PERSONAL NAME | |
| Personal name | Tromba, Anthony. |
| Relator term | author. |
| 245 12 - TITLE STATEMENT | |
| Title | A Theory of Branched Minimal Surfaces |
| Medium | [electronic resource] / |
| Statement of responsibility, etc | by Anthony Tromba. |
| 264 #1 - | |
| -- | Berlin, Heidelberg : |
| -- | Springer Berlin Heidelberg, |
| -- | 2012. |
| 300 ## - PHYSICAL DESCRIPTION | |
| Extent | IX, 191p. 2 illus. |
| Other physical details | online resource. |
| 336 ## - | |
| -- | text |
| -- | txt |
| -- | rdacontent |
| 337 ## - | |
| -- | computer |
| -- | c |
| -- | rdamedia |
| 338 ## - | |
| -- | online resource |
| -- | cr |
| -- | rdacarrier |
| 347 ## - | |
| -- | text file |
| -- | |
| -- | rda |
| 490 1# - SERIES STATEMENT | |
| Series statement | Springer Monographs in Mathematics, |
| International Standard Serial Number | 1439-7382 |
| 505 0# - FORMATTED CONTENTS NOTE | |
| Formatted contents note | 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. |
| 520 ## - SUMMARY, ETC. | |
| Summary, etc | 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. |
| 650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM | |
| Topical term or geographic name as entry element | Mathematics. |
| 650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM | |
| Topical term or geographic name as entry element | Functions of complex variables. |
| 650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM | |
| Topical term or geographic name as entry element | Global analysis. |
| 650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM | |
| Topical term or geographic name as entry element | Sequences (Mathematics). |
| 650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM | |
| Topical term or geographic name as entry element | Global differential geometry. |
| 650 14 - SUBJECT ADDED ENTRY--TOPICAL TERM | |
| Topical term or geographic name as entry element | Mathematics. |
| 650 24 - SUBJECT ADDED ENTRY--TOPICAL TERM | |
| Topical term or geographic name as entry element | Functions of a Complex Variable. |
| 650 24 - SUBJECT ADDED ENTRY--TOPICAL TERM | |
| Topical term or geographic name as entry element | Sequences, Series, Summability. |
| 650 24 - SUBJECT ADDED ENTRY--TOPICAL TERM | |
| Topical term or geographic name as entry element | Differential Geometry. |
| 650 24 - SUBJECT ADDED ENTRY--TOPICAL TERM | |
| Topical term or geographic name as entry element | Global Analysis and Analysis on Manifolds. |
| 710 2# - ADDED ENTRY--CORPORATE NAME | |
| Corporate name or jurisdiction name as entry element | SpringerLink (Online service) |
| 773 0# - HOST ITEM ENTRY | |
| Title | Springer eBooks |
| 776 08 - ADDITIONAL PHYSICAL FORM ENTRY | |
| Display text | Printed edition: |
| International Standard Book Number | 9783642256196 |
| 830 #0 - SERIES ADDED ENTRY--UNIFORM TITLE | |
| Uniform title | Springer Monographs in Mathematics, |
| -- | 1439-7382 |
| 856 40 - ELECTRONIC LOCATION AND ACCESS | |
| Uniform Resource Identifier | http://dx.doi.org/10.1007/978-3-642-25620-2 |
| 912 ## - | |
| -- | ZDB-2-SMA |
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