Energy of knots and conformal geometry:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Singapore [u.a.]
World Scientific
2003
|
| Schriftenreihe: | Series on knots and everything
33 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Includes bibliographical references and index |
| Beschreibung: | XIV, 288 S. graph. Darst. |
| ISBN: | 9812383166 |
Internformat
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| 100 | 1 | |a O'Hara, Jun |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Energy of knots and conformal geometry |c Jun O'Hara |
| 264 | 1 | |a Singapore [u.a.] |b World Scientific |c 2003 | |
| 300 | |a XIV, 288 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Series on knots and everything |v 33 | |
| 500 | |a Includes bibliographical references and index | ||
| 650 | 4 | |a Géométrie conforme | |
| 650 | 4 | |a Nuds, Théorie des | |
| 650 | 4 | |a Conformal geometry | |
| 650 | 4 | |a Knot theory | |
| 650 | 0 | 7 | |a Energie |0 (DE-588)4014692-3 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Knotentheorie |0 (DE-588)4164318-5 |2 gnd |9 rswk-swf |
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| 689 | 0 | 2 | |a Energie |0 (DE-588)4014692-3 |D s |
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Datensatz im Suchindex
| _version_ | 1804129803371020288 |
|---|---|
| adam_text | K(#E SERIES ON KNOTS AND EVERYTHING * VOL. 33 ENERGY OF KNOTS AND
CONFORMAL GEOMETRY JUN O HARA DEPARTMENT OF MATHEMATICS TOKYO
METROPOLITAN UNIVERSITY JAPAN WORLD SCIENTIFIC NEW JERSEY LONDON *
SINGAPORE * HONG KONG CONTENTS PART 1 IN SEARCH OF THE OPTIMAL
EMBEDDING OF A KNOT 1 CHAPTER 1 INTRODUCTION 3 1.1 MOTIVATIONAL PROBLEM
3 1.2 NOTATIONS AND REMARKS 8 CHAPTER 2 A-ENERGY FUNCTIONAL E^ 9 2.1
RENORMALIZATIONS OF ELECTROSTATIC ENERGY OF CHARGED KNOTS ... 9 2.2
RENORMALIZATIONS OF R~ A -MODIFIED ELECTROSTATIC ENERGY, E^ . . 15 2.3
ASYMPTOTIC BEHAVIOR OF R~ A ENERGY OF POLYGONAL KNOTS 22 2.4 THE
SELF-REPULSIVENESS OF (A) 26 CHAPTER 3 ON E^ 31 3.1 CONTINUITY 31 3.2
BEHAVIOR OF E^ UNDER PULL-TIGHT 34 3.3 MOBIUS INVARIANCE 34 3.4 THE
COSINE FORMULA FOR E^ 35 3.5 EXISTENCE OF E^ MINIMIZERS 42 3.6 AVERAGE
CROSSING NUMBER AND FINITENESS OF KNOT TYPES 44 3.7 GRADIENT,
REGULARITY OF E^ MINIMIZERS, AND CRITERION OF CRITICALITY 45 3.8
UNSTABLE U (2) -CRITICAL TORUS KNOTS 54 3.9 ENERGY ASSOCIATED TO A
DIAGRAM 57 XI XII CONTENTS 3.9.1 GENERAL FRAMEWORK 58 3.9.2 X-ENERGY
59 3.10 NORMAL PROJECTION ENERGIES 60 3.11 GENERALIZATION TO HIGHER
DIMENSIONS 60 CHAPTER 4 L NORM ENERGY WITH HIGHER INDEX 63 4.1
DEFINITION OF (A, P)-ENERGY FUNCTIONAL FOR KNOTS E A P 63 4.2 CONTROL OF
KNOTS BY E A P {E AP ) 65 4.3 COMPLETE SYSTEM OF ADMISSIBLE SOLID TORI
AND FINITENESS OF KNOT TYPES 75 4.4 EXISTENCE OF E A P MINIMIZERS 77
4.5 THE CIRCLES MINIMIZE E A P 78 4.6 DEFINITION OF A-ENERGY
POLYNOMIAL FOR KNOTS 79 4.7 BRYLINSKI S BETA FUNCTION FOR KNOTS 79 4.8
OTHER L -NORM ENERGIES 81 CHAPTER 5 NUMERICAL EXPERIMENTS 83 5.1
NUMERICAL EXPERIMENTS ON E^ 84 5.2 A 2 CASES. THE LIMIT AS N - * OO
WHEN A 3 84 5.3 TABLE OF APPROXIMATE MINIMUM ENERGIES 86 CHAPTER 6
STEREO PICTURES OF E^ MINIMIZERS 91 CHAPTER 7 ENERGY OF KNOTS IN A
RIEMANNIAN MANIFOLD 101 7.1 DEFINITION OF THE UNIT DENSITY (A, P)-ENERGY
E^F 101 7.2 CONTROL OF KNOTS BY E A J 102 7.3 EXISTENCE OF ENERGY
MINIMIZERS 105 7.4 EXAMPLES : ENERGY OF KNOTS IN S 3 AND H 3 107 7.4.1
ENERGY OF CIRCLES IN S 3 107 7.4.2 ENERGY OF TREFOILS ON CLIFFORD TORI
IN S 3 109 7.4.3 EXISTENCE OF E S I MINIMIZERS 109 7.4.4 ENERGY OF KNOTS
IN M 3 110 7.5 OTHER DEFINITIONS 114 7.6 THE EXISTENCE OF ENERGY
MINIMIZERS 115 CHAPTER 8 PHYSICAL KNOT ENERGIES 117 8.1 THICKNESS AND
ROPELENGTH 117 8.2 FOUR THIRDS LAW 118 8.3 OSCULATING CIRCLES AND
OSCULATING SPHERES 119 CONTENTS XIII 8.4 GLOBAL RADIUS OF CURVATURE 121
8.5 SELF DISTANCE TYPE ENERGIES DEFINED VIA THE DISTANCE FUNCTION . .
127 8.6 RELATION BETWEEN THESE GEOMETRIC QUANTITIES AND E A P 131 8.7
NUMERICAL COMPUTATIONS AND APPLICATIONS 132 PART 2 ENERGY OF KNOTS FROM
A CONFORMAL GEOMETRIC VIEWPOINT 133 CHAPTER 9 PREPARATION FROM CONFORMAL
GEOMETRY 135 9.1 THE LORENTZIAN METRIC ON MINKOWSKI SPACE 135 9.2 THE
LORENTZIAN EXTERIOR PRODUCT 143 9.3 THE SPACE OF SPHERES 144 9.4 THE
4-TUPLE MAP AND THE CROSS RATIO OF 4 POINTS 147 9.5 PENCILS OF SPHERES
151 9.6 MODULUS OF AN ANNULUS 156 9.7 CROSS-SEPARATING ANNULI AND THE
MODULUS OF FOUR POINTS . . . . 158 9.8 THE MEASURE ON THE SPACE OF
SPHERES A 165 9.9 ORIENTATIONS OF 2-SPHERES 168 CHAPTER 10 THE SPACE OF
NON-TRIVIAL SPHERES OF A KNOT 175 10.1 NON-TRIVIAL SPHERES OF A KNOT 175
10.2 THE 4-TUPLE MAP FOR A KNOT 177 10.3 GENERALIZATION OF THE 4-TUPLE
MAP TO THE DIAGONAL 179 10.3.1 TWICE TANGENT SPHERES 179 10.3.2 TANGENT
SPHERES 183 10.3.3 OSCULATING SPHERES 184 10.4 LOWER SEMI-CONTINUITY OF
THE RADII OF NON-TRIVIAL SPHERES .... 186 CHAPTER 11 THE INFINITESIMAL
CROSS RATIO 189 11.1 THE INFINITESIMAL CROSS RATIO OF THE COMPLEX PLANE
189 11.2 THE REAL PART AS THE CANONICAL SYMPLECTIC FORM OF T*S 2 . . .
. 191 11.3 THE INFINITESIMAL CROSS RATIO FOR A KNOT 201 11.4 FROM THE
COSINE FORMULA TO THE ORIGINAL DEFINITION OF E^ . . . 205 11.5 M 2)
-ENERGY FOR LINKS 207 CHAPTER 12 THE CONFORMAL SIN ENERGY E SM $ 213
12.1 THE PROJECTION OF THE INVERTED OPEN KNOT 213 12.2 THE GEOMETRIC
MEANING OF E S I N G 215 XIV CONTENTS 12.3 SELF-REPULSIVENESS OF E S J N
G 216 12.4 E S U E AND THE AVERAGE CROSSING NUMBER 221 12.5 E SINE FOR
LINKS 221 CHAPTER 13 MEASURE OF NON-TRIVIAL SPHERES 223 13.1 NON-TRIVIAL
SPHERES, TANGENT SPHERES AND TWICE TANGENT SPHERES 223 13.2 THE VOLUME
OF THE SET OF THE NON-TRIVIAL SPHERES 224 13.3 THE MEASURE OF
NON-TRIVIAL SPHERES IN TERMS OF THE INFINITESIMAL CROSS RATIO 226 13.4
NON-TRIVIAL ANNULI AND THE MODULUS OF A KNOT ._-23-L- 13.5
SELF-REPULSIVENESS OF THE MEASURE OF NON-TRIVIAL SPHERES 235 13.6 THE
MEASURE OF NON-TRIVIAL SPHERES FOR NON-TRIVIAL KNOTS . . . . 237 13.7
MEASURE OF NON-TRIVIAL SPHERES FOR LINKS 241 APPENDIX A GENERALIZATION
OF THE GAUSS FORMULA FOR THE LINK- ING NUMBER 243 A.I THE GAUSS FORMULA
FOR THE LINKING NUMBER 243 A.2 THE WRITHE AND THE SELF-LINKING NUMBER
245 A.3 THE TOTAL TWIST 247 A.4 AVERAGE CROSSING NUMBER 249 A.5 THE
CONFORMAL ANGLE AND THE GAUSS INTEGRAL 250 A.6 MOBIUS INVARIANCE OF THE
WRITHE 252 A.7 THE CIRCULAR GAUSS MAP AND THE INVERTED OPEN KNOTS 253
APPENDIX B THE 3-TUPLE MAP TO THE SET OF CIRCLES IN 5 3 257 B.I THE SET
OF UNORIENTED CIRCLES IN S 3 257 B.2 THE 3-TUPLE MAP TO THE SET OF
CIRCLES 257 APPENDIX C CONFORMAL MODULI OF A SOLID TORUS 259 C.I MODULUS
OF A 2-DIMENSIONAL ANNULUS REVISITED 259 C.2 CONFORMAL MODULI OF A SOLID
TORUS 260 APPENDIX D KIRCHHOFF ELASTICA 263 APPENDIX E OPEN PROBLEMS AND
DREAMS 265 BIBLIOGRAPHY 271 INDEX 285
|
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| ctrlnum | (OCoLC)51478044 (DE-599)BVBBV016475335 |
| dewey-full | 514/.224 |
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| dewey-ones | 514 - Topology |
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| dewey-search | 514/.224 |
| dewey-sort | 3514 3224 |
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| id | DE-604.BV016475335 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T19:10:56Z |
| institution | BVB |
| isbn | 9812383166 |
| language | English |
| lccn | 2003041104 |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-010185674 |
| oclc_num | 51478044 |
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| owner_facet | DE-355 DE-BY-UBR DE-703 DE-19 DE-BY-UBM DE-11 |
| physical | XIV, 288 S. graph. Darst. |
| publishDate | 2003 |
| publishDateSearch | 2003 |
| publishDateSort | 2003 |
| publisher | World Scientific |
| record_format | marc |
| series | Series on knots and everything |
| series2 | Series on knots and everything |
| spelling | O'Hara, Jun Verfasser aut Energy of knots and conformal geometry Jun O'Hara Singapore [u.a.] World Scientific 2003 XIV, 288 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Series on knots and everything 33 Includes bibliographical references and index Géométrie conforme Nuds, Théorie des Conformal geometry Knot theory Energie (DE-588)4014692-3 gnd rswk-swf Knotentheorie (DE-588)4164318-5 gnd rswk-swf Konforme Struktur (DE-588)4500911-9 gnd rswk-swf Knotentheorie (DE-588)4164318-5 s Konforme Struktur (DE-588)4500911-9 s Energie (DE-588)4014692-3 s DE-604 Series on knots and everything 33 (DE-604)BV004608347 33 GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=010185674&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | O'Hara, Jun Energy of knots and conformal geometry Series on knots and everything Géométrie conforme Nuds, Théorie des Conformal geometry Knot theory Energie (DE-588)4014692-3 gnd Knotentheorie (DE-588)4164318-5 gnd Konforme Struktur (DE-588)4500911-9 gnd |
| subject_GND | (DE-588)4014692-3 (DE-588)4164318-5 (DE-588)4500911-9 |
| title | Energy of knots and conformal geometry |
| title_auth | Energy of knots and conformal geometry |
| title_exact_search | Energy of knots and conformal geometry |
| title_full | Energy of knots and conformal geometry Jun O'Hara |
| title_fullStr | Energy of knots and conformal geometry Jun O'Hara |
| title_full_unstemmed | Energy of knots and conformal geometry Jun O'Hara |
| title_short | Energy of knots and conformal geometry |
| title_sort | energy of knots and conformal geometry |
| topic | Géométrie conforme Nuds, Théorie des Conformal geometry Knot theory Energie (DE-588)4014692-3 gnd Knotentheorie (DE-588)4164318-5 gnd Konforme Struktur (DE-588)4500911-9 gnd |
| topic_facet | Géométrie conforme Nuds, Théorie des Conformal geometry Knot theory Energie Knotentheorie Konforme Struktur |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=010185674&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV004608347 |
| work_keys_str_mv | AT oharajun energyofknotsandconformalgeometry |