Harmonic maps, conservation laws, and moving frames / (Record no. 518583)
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| 000 -LEADER | |
|---|---|
| fixed length control field | 04709nam a22003978i 4500 |
| 001 - CONTROL NUMBER | |
| control field | CR9780511543036 |
| 003 - CONTROL NUMBER IDENTIFIER | |
| control field | UkCbUP |
| 005 - DATE AND TIME OF LATEST TRANSACTION | |
| control field | 20200124160241.0 |
| 006 - FIXED-LENGTH DATA ELEMENTS--ADDITIONAL MATERIAL CHARACTERISTICS--GENERAL INFORMATION | |
| fixed length control field | m|||||o||d|||||||| |
| 007 - PHYSICAL DESCRIPTION FIXED FIELD--GENERAL INFORMATION | |
| fixed length control field | cr|||||||||||| |
| 008 - FIXED-LENGTH DATA ELEMENTS--GENERAL INFORMATION | |
| fixed length control field | 090505s2002||||enk o ||1 0|eng|d |
| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER | |
| International Standard Book Number | 9780511543036 (ebook) |
| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER | |
| Cancelled/invalid ISBN | 9780521811606 (hardback) |
| 040 ## - CATALOGING SOURCE | |
| Original cataloging agency | UkCbUP |
| Language of cataloging | eng |
| Description conventions | rda |
| Transcribing agency | UkCbUP |
| 041 1# - LANGUAGE CODE | |
| Language code of text/sound track or separate title | eng |
| Language code of original and/or intermediate translations of text | fre |
| 050 00 - LIBRARY OF CONGRESS CALL NUMBER | |
| Classification number | QA614.73 |
| Item number | .H45 2002 |
| 082 00 - DEWEY DECIMAL CLASSIFICATION NUMBER | |
| Classification number | 514/.74 |
| Edition number | 21 |
| 100 1# - MAIN ENTRY--PERSONAL NAME | |
| Personal name | Hélein, Frédéric, |
| Dates associated with a name | 1963- |
| Relator term | author. |
| 245 10 - TITLE STATEMENT | |
| Title | Harmonic maps, conservation laws, and moving frames / |
| Statement of responsibility, etc | Frédéric Hélein. |
| 246 3# - VARYING FORM OF TITLE | |
| Title proper/short title | Harmonic Maps, Conservation Laws & Moving Frames |
| 250 ## - EDITION STATEMENT | |
| Edition statement | Second edition. |
| 264 #1 - Production, Publication, Distribution, Manufacture, and Copyright Notice (R) | |
| Place of production, publication, distribution, manufacture (R) | Cambridge : |
| Name of producer, publisher, distributor, manufacturer (R) | Cambridge University Press, |
| Date of production, publication, distribution, manufacture, or copyright notice | 2002. |
| 300 ## - PHYSICAL DESCRIPTION | |
| Extent | 1 online resource (xxv, 264 pages) : |
| Other physical details | digital, PDF file(s). |
| 336 ## - Content Type (R) | |
| Content type term (R) | text |
| Content type code (R) | txt |
| Source (NR) | rdacontent |
| 337 ## - Media Type (R) | |
| Media type term (R) | computer |
| Media type code (R) | c |
| Source (NR) | rdamedia |
| 338 ## - Carrier Type (R) | |
| Carrier type term (R) | online resource |
| Carrier type code (R) | cr |
| Source (NR) | rdacarrier |
| 490 1# - SERIES STATEMENT | |
| სერიის ცნობა | Cambridge tracts in mathematics ; |
| Volume number/sequential designation | 150 |
| 500 ## - GENERAL NOTE | |
| General note | Title from publisher's bibliographic system (viewed on 05 Oct 2015). |
| 505 00 - FORMATTED CONTENTS NOTE | |
| Miscellaneous information | 1 |
| Title | Geometric and analytic setting |
| Miscellaneous information | 1 -- |
| -- | 1.1 |
| Title | The Laplacian on (M, g) |
| Miscellaneous information | 2 -- |
| -- | 1.2 |
| Title | Harmonic maps between two Riemannian manifolds |
| Miscellaneous information | 5 -- |
| -- | 1.3 |
| Title | Conservation laws for harmonic maps |
| Miscellaneous information | 11 -- |
| -- | 1.3.1 |
| Title | Symmetries on N |
| Miscellaneous information | 12 -- |
| -- | 1.3.2 |
| Title | Symmetries on M: the stress-energy tensor |
| Miscellaneous information | 18 -- |
| -- | 1.3.3 |
| Title | Consequences of theorem 1.3.6 |
| Miscellaneous information | 24 -- |
| -- | 1.4 |
| Title | Variational approach: Sobolev spaces |
| Miscellaneous information | 31 -- |
| -- | 1.4.1 |
| Title | Weakly harmonic maps |
| Miscellaneous information | 37 -- |
| -- | 1.4.2 |
| Title | Weakly Noether harmonic maps |
| Miscellaneous information | 42 -- |
| -- | 1.4.3 |
| Title | Minimizing maps |
| Miscellaneous information | 42 -- |
| -- | 1.4.4 |
| Title | Weakly stationary maps |
| Miscellaneous information | 43 -- |
| -- | 1.4.5 |
| Title | Relation between these different definitions |
| Miscellaneous information | 43 -- |
| -- | 1.5 |
| Title | Regularity of weak solutions |
| Miscellaneous information | 46 -- |
| -- | 2 |
| Title | Harmonic maps with symmetry |
| Miscellaneous information | 49 -- |
| -- | 2.1 |
| Title | Backlund transformation |
| Miscellaneous information | 50 -- |
| -- | 2.1.1 |
| Title | S[superscript 2]-valued maps |
| Miscellaneous information | 50 -- |
| -- | 2.1.2 |
| Title | Maps taking values in a sphere S[superscript n], n [greater than or equal] 2 |
| Miscellaneous information | 54 -- |
| -- | 2.1.3 |
| Title | Comparison |
| Miscellaneous information | 56 -- |
| -- | 2.2 |
| Title | Harmonic maps with values into Lie groups |
| Miscellaneous information | 58 -- |
| -- | 2.2.1 |
| Title | Families of curvature-free connections |
| Miscellaneous information | 65 -- |
| -- | 2.2.2 |
| Title | The dressing |
| Miscellaneous information | 72 -- |
| -- | 2.2.3 |
| Title | Uhlenbeck factorization for maps with values in U(n) |
| Miscellaneous information | 77 -- |
| -- | 2.2.4 |
| Title | S[superscript 1]-action |
| Miscellaneous information | 79 -- |
| -- | 2.3 |
| Title | Harmonic maps with values into homogeneous spaces |
| Miscellaneous information | 82 -- |
| -- | 2.4 |
| Title | Synthesis: relation between the different formulations |
| Miscellaneous information | 95 -- |
| -- | 2.5 |
| Title | Compactness of weak solutions in the weak topology |
| Miscellaneous information | 101 -- |
| -- | 2.6 |
| Title | Regularity of weak solutions |
| Miscellaneous information | 109 -- |
| -- | 3 |
| Title | Compensations and exotic function spaces |
| Miscellaneous information | 114 -- |
| -- | 3.1 |
| Title | Wente's inequality |
| Miscellaneous information | 115 -- |
| -- | 3.1.1 |
| Title | The inequality on a plane domain |
| Miscellaneous information | 115 -- |
| -- | 3.1.2 |
| Title | The inequality on a Riemann surface |
| Miscellaneous information | 119 -- |
| -- | 3.2 |
| Title | Hardy spaces |
| Miscellaneous information | 128 -- |
| -- | 3.3 |
| Title | Lorentz spaces |
| Miscellaneous information | 135 -- |
| -- | 3.4 |
| Title | Back to Wente's inequality |
| Miscellaneous information | 145 -- |
| -- | 3.5 |
| Title | Weakly stationary maps with values into a sphere |
| Miscellaneous information | 150 -- |
| -- | 4 |
| Title | Harmonic maps without symmetry |
| Miscellaneous information | 165 -- |
| -- | 4.1 |
| Title | Regularity of weakly harmonic maps of surfaces |
| Miscellaneous information | 166 -- |
| -- | 4.2 |
| Title | Generalizations in dimension 2 |
| Miscellaneous information | 187 -- |
| -- | 4.3 |
| Title | Regularity results in arbitrary dimension |
| Miscellaneous information | 193 -- |
| -- | 4.4 |
| Title | Conservation laws for harmonic maps without symmetry |
| Miscellaneous information | 205 -- |
| -- | 4.4.1 |
| Title | Conservation laws |
| Miscellaneous information | 206 -- |
| -- | 4.4.2 |
| Title | Isometric embedding of vector-bundle-valued differential forms |
| Miscellaneous information | 211 -- |
| -- | 4.4.3 |
| Title | A variational formulation for the case m = n = 2 and p = 1 |
| Miscellaneous information | 215 -- |
| -- | 4.4.4 |
| Title | Hidden symmetries for harmonic maps on surfaces? |
| Miscellaneous information | 218 -- |
| -- | 5 |
| Title | Surfaces with mean curvature in L[superscript 2] |
| Miscellaneous information | 221 -- |
| -- | 5.1 |
| Title | Local results |
| Miscellaneous information | 224 -- |
| -- | 5.2 |
| Title | Global results |
| Miscellaneous information | 237 -- |
| -- | 5.3 |
| Title | Willmore surfaces |
| Miscellaneous information | 242 -- |
| -- | 5.4 |
| Title | Epilogue: Coulomb frames and conformal coordinates |
| Miscellaneous information | 244. |
| 520 ## - SUMMARY, ETC. | |
| Summary, etc | The author presents an accessible and self-contained introduction to harmonic map theory and its analytical aspects, covering recent developments in the regularity theory of weakly harmonic maps. The book begins by introducing these concepts, stressing the interplay between geometry, the role of symmetries and weak solutions. The reader is then presented with a guided tour into the theory of completely integrable systems for harmonic maps, followed by two chapters devoted to recent results on the regularity of weak solutions. A self-contained presentation of 'exotic' functional spaces from the theory of harmonic analysis is given and these tools are then used for proving regularity results. The importance of conservation laws is stressed and the concept of a 'Coulomb moving frame' is explained in detail. The book ends with further applications and illustrations of Coulomb moving frames to the theory of surfaces. |
| 650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM | |
| Topical term or geographic name as entry element | Harmonic maps. |
| 650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM | |
| Topical term or geographic name as entry element | Riemannian manifolds. |
| 776 08 - ADDITIONAL PHYSICAL FORM ENTRY | |
| Display text | Print version: |
| International Standard Book Number | 9780521811606 |
| 830 #0 - SERIES ADDED ENTRY--UNIFORM TITLE | |
| Uniform title | Cambridge tracts in mathematics ; |
| Volume number/sequential designation | 150. |
| 856 40 - ELECTRONIC LOCATION AND ACCESS | |
| Uniform Resource Identifier | <a href="https://doi.org/10.1017/CBO9780511543036">https://doi.org/10.1017/CBO9780511543036</a> |
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