Variational problems in geometry:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English Japanese |
| Veröffentlicht: |
Providence, RI
Amer. Math. Soc.
2002
|
| Schriftenreihe: | Translations of mathematical monographs
205 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XVII, 209 S. |
| ISBN: | 0821813560 9780821813560 |
Internformat
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Datensatz im Suchindex
| _version_ | 1804128923709079552 |
|---|---|
| adam_text | CO A C DC TRANSLATIONS OF MATHEMATICAL MONOGRAPHS VOLUME 205 0) 2 CO
VARIATIONAL PROBLEMS W IN GEOMETRY SEIKI NISHIKAWA TRANSLATED BY KINETSU
ABE AMERICAN MATHEMATICAL SOCIETY PROVIDENCE, RHODE ISLAND CONTENTS
PREFACE TO THE ENGLISH EDITION VII PREFACE IX OUTLINES AND OBJECTIVES OF
THE THEORY XIII CHAPTER 1. ARC LENGTH OF CURVES AND GEODESIES 1 1.1. ARC
LENGTH AND ENERGY OF CURVES 1 1.2. EULER S EQUATION 9 1.3. CONNECTIONS
AND COVARIANT DIFFERENTIATION 16 1.4. GEODESIES 28 1.5. MINIMAL LENGTH
PROPERTY OF GEODESIES 38 SUMMARY 43 EXERCISES 44 CHAPTER 2. FIRST AND
SECOND VARIATION FORMULAS 47 2.1. THE FIRST VARIATION FORMULA 47 2.2.
CURVATURE TENSOR 54 2.3. THE SECOND VARIATION FORMULA 65 2.4. EXISTENCE
OF MINIMAL GEODESIES 69 2.5. APPLICATIONS TO RIEMANNIAN GEOMETRY 77
SUMMARY 82 EXERCISES 82 CHAPTER 3. ENERGY OF MAPS AND HARMONIC MAPS 85
3.1. ENERGY OF MAPS 85 3.2. TENSION FIELDS 90 3.3. THE FIRST VARIATION
FORMULA 99 3.4. HARMONIC MAPS 103 3.5. THE SECOND VARIATION FORMULA 110
SUMMARY 114 EXERCISE 114 VI CONTENTS CHAPTER 4. EXISTENCE OF HARMONIC
MAPS 119 4.1. THE HEAT FLOW METHOD 119 4.2. EXISTENCE OF LOCAL
TIME-DEPENDENT SOLUTIONS 130 4.3. EXISTENCE OF GLOBAL TIME-DEPENDENT
SOLUTIONS 141 4.4. EXISTENCE AND UNIQUENESS OF HARMONIC MAPS 150 4.5.
APPLICATIONS TO RIEMANNIAN GEOMETRY 155 SUMMARY 160 EXERCISES 160
APPENDIX A. FUNDAMENTALS OF THE THEORY OF MANIFOLDS AND FUNCTIONAL
ANALYSIS 163 A.I. FUNDAMENTALS OF MANIFOLDS 163 A.2. FUNDAMENTALS OF
FUNCTIONAL ANALYSIS 173 PROSPECTS FOR CONTEMPORARY MATHEMATICS 183
SOLUTIONS TO EXERCISE PROBLEMS 187 BIBLIOGRAPHY 201 INDEX 207
|
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| illustrated | Not Illustrated |
| indexdate | 2024-07-09T18:56:57Z |
| institution | BVB |
| isbn | 0821813560 9780821813560 |
| language | English Japanese |
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| physical | XVII, 209 S. |
| publishDate | 2002 |
| publishDateSearch | 2002 |
| publishDateSort | 2002 |
| publisher | Amer. Math. Soc. |
| record_format | marc |
| series | Translations of mathematical monographs |
| series2 | Translations of mathematical monographs Iwanami series in modern mathematics |
| spelling | Nishikawa, Seiki Verfasser aut Kikagakuteki henbun mondai Variational problems in geometry Seiki Nishikawa Providence, RI Amer. Math. Soc. 2002 XVII, 209 S. txt rdacontent n rdamedia nc rdacarrier Translations of mathematical monographs 205 Iwanami series in modern mathematics Applications harmoniques Inégalités variationnelles Riemann, Variétés de Variatieproblemen gtt Harmonic maps Riemannian manifolds Variational inequalities (Mathematics) Riemannscher Raum (DE-588)4128295-4 gnd rswk-swf Variationsungleichung (DE-588)4187420-1 gnd rswk-swf Variationsungleichung (DE-588)4187420-1 s Riemannscher Raum (DE-588)4128295-4 s DE-604 Translations of mathematical monographs 205 (DE-604)BV000002394 205 GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009630566&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Nishikawa, Seiki Variational problems in geometry Translations of mathematical monographs Applications harmoniques Inégalités variationnelles Riemann, Variétés de Variatieproblemen gtt Harmonic maps Riemannian manifolds Variational inequalities (Mathematics) Riemannscher Raum (DE-588)4128295-4 gnd Variationsungleichung (DE-588)4187420-1 gnd |
| subject_GND | (DE-588)4128295-4 (DE-588)4187420-1 |
| title | Variational problems in geometry |
| title_alt | Kikagakuteki henbun mondai |
| title_auth | Variational problems in geometry |
| title_exact_search | Variational problems in geometry |
| title_full | Variational problems in geometry Seiki Nishikawa |
| title_fullStr | Variational problems in geometry Seiki Nishikawa |
| title_full_unstemmed | Variational problems in geometry Seiki Nishikawa |
| title_short | Variational problems in geometry |
| title_sort | variational problems in geometry |
| topic | Applications harmoniques Inégalités variationnelles Riemann, Variétés de Variatieproblemen gtt Harmonic maps Riemannian manifolds Variational inequalities (Mathematics) Riemannscher Raum (DE-588)4128295-4 gnd Variationsungleichung (DE-588)4187420-1 gnd |
| topic_facet | Applications harmoniques Inégalités variationnelles Riemann, Variétés de Variatieproblemen Harmonic maps Riemannian manifolds Variational inequalities (Mathematics) Riemannscher Raum Variationsungleichung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009630566&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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| work_keys_str_mv | AT nishikawaseiki kikagakutekihenbunmondai AT nishikawaseiki variationalproblemsingeometry |