Riemannian geometry and geometric analysis:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Berlin [u.a.]
Springer
2011
|
| Edition: | 6. ed. |
| Series: | Universitext
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XIII, 611 S. graph. Darst. |
| ISBN: | 9783642212970 |
Staff View
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Record in the Search Index
| _version_ | 1804148337652269056 |
|---|---|
| adam_text | IMAGE 1
CONTENTS
RIEMANNIAN MANIFOLDS I 1.1 MANIFOLDS AND DIFFCRENTIABLE MANIFOLDS 11.2
TANGENT SPACES 61.3 SUBMANIFOLDS 101.4 RIEMANNIAN METRICS 131.5
EXISTENCE OF GEODESIES ON COMPACT MANIFOLDS 281.6 THE HEAT FLOW AND THE
EXISTENCE OF GEODESIES 31 1.7 EXISTENCE OF GEODESIES ON COMPLETE
MANIFOLDS 35 EXERCISES FOR CHAPTER 1 37 LIE GROUPS AND VECTOR BUNDLES 41
2.1 VECTOR BUNDLES 412.2 INTEGRAL CURVES OF VECTOR FIELDS. LIE ALGEBRAS
512.3 LIE GROUPS 612.4 SPIN STRUCTURES 67EXERCISES FOR CHAPTER 2 87 THE
LAPLACE OPERATOR AND HARMONIC DIFFERENTIAL FORMS 89 3.1 THE LAPLACE
OPERATOR ON FUNCTIONS 893.2 THE SPECTRUM OF THE LAPLACE OPERATOR 943.3
THE LAPLACE OPERATOR ON FORMS 1023.4 REPRESENTING COHOMOLOGY CLASSES BY
HARMONIC FORMS 113 3.5 GENERALIZATIONS 1223.6 THE HEAT FLOW AND HARMONIC
FORMS 123EXERCISES FOR CHAPTER 3 129 CONNECTIONS AND CURVATURE 133 4.1
CONNECTIONS IN VECTOR BUNDLES 1334.2 METRIC CONNECTIONS. THE YANG-MILLS
FUNCTIONAL 1444.3 THE LEVI-CIVITA CONNECTION 1604.4 CONNECTIONS FOR SPIN
STRUCTURES AND THE DIRAC OPERATOR 175 4.5 THE BOCHNER METHOD 182
BIBLIOGRAFISCHE INFORMATIONEN HTTP://D-NB.INFO/1011273225 DIGITALISIERT
DURCH
IMAGE 2
CONTENTS
4.6 EIGENVALUE ESTIMATES BY THE METHOD OF LI-YAU 187
4.7 THE GEOMETRY OF SUBMANIFOLDS 191
4.8 MINIMAL SUBMANIFOLDS 196
EXERCISES FOR CHAPTER 4 203
5 GEODESIES AND JACOBI FIELDS 205
5.1 FIRST AND SECOND VARIATION OF ARC LENGTH AND ENERGY 205
5.2 JACOBI FIELDS 211
5.3 CONJUGATE POINTS AND DISTANCE MINIMIZING GEODESIES 219
5.4 RIEMANNIAN MANIFOLDS OF CONSTANT CURVATURE 227
5.5 THE RAUCH COMPARISON THEOREMS AND OTHER JACOBI FIELD ESTIMATES . 229
5.6 GEOMETRIC APPLICATIONS OF JACOBI FIELD ESTIMATES 234
5.7 APPROXIMATE FUNDAMENTAL SOLUTIONS AND REPRESENTATION FORMULAS . .
239 5.8 THE GEOMETRY OF MANIFOLDS OF NONPOSITIVE SECTIONAL CURVATURE . .
.. 241 EXERCISES FOR CHAPTER 5 258
A SHORT SURVEY ON CURVATURE AND TOPOLOGY 261
6 SYMMETRIC SPACES AND KAHLER MANIFOLDS 269
6.1 COMPLEX PROJECTIVE SPACE 269
6.2 KAHLER MANIFOLDS 275
6.3 THE GEOMETRY OF SYMMETRIC SPACES 285
6.4 SOME RESULTS ABOUT THE STRUCTURE OF SYMMETRIC SPACES 296
6.5 THE SPACE SL(N,R)/SO(N,R) 303
6.6 SYMMETRIC SPACES OF NONCOMPACT TYPE 320
EXERCISES FOR CHAPTER 6 325
7 MORSE THEORY AND FLOER HOMOLOGY 327
7.1 PRELIMINARIES: AIMS OF MORSE THEORY 327
7.2 THE PALAIS-SMALE CONDITION, EXISTENCE OF SADDLE POINTS 332
7.3 LOCAL ANALYSIS 334
7.4 LIMITS OF TRAJECTORIES OF THE GRADIENT FLOW 350
7.5 FLOER CONDITION, TRANSVERSALITY AND Z2-COHOMOLOGY 358
7.6 ORIENTATIONS AND Z-HOMOLOGY 364
7.7 HOMOTOPIES 368
7.8 GRAPH FLOWS 372
7.9 ORIENTATIONS 376
7.10 THE MORSE INEQUALITIES 392
7.11 THE PALAIS-SMALE CONDITION AND THE EXISTENCE OF CLOSED GEODESIES .
. 403 EXERCISES FOR CHAPTER 7 416
8 HARMONIC MAPS BETWEEN RIEMANNIAN MANIFOLDS 419
8.1 DEFINITIONS 419
8.2 FORMULAS FOR HARMONIC MAPS. THE BOCHNER TECHNIQUE 426
8.3 THE ENERGY INTEGRAL AND WEAKLY HARMONIC MAPS 438
8.4 HIGHER REGULARITY 448
IMAGE 3
CONTENTS XIII
8.5 EXISTENCE OF HARMONIE MAPS FOR NONPOSITIVE CURVATURE 459
8.6 REGULARITY OF HARMONIC MAPS FOR NONPOSITIVE CURVATURE 466 8.7
HARMONIC MAP UNIQUENESS AND APPLICATIONS 485
EXERCISES FOR CHAPTER 8 492
9 HARMONIC MAPS FROM RIEMANN SURFACES 495
9.1 TWO-DIMENSIONAL HARMONIC MAPPINGS 495
9.2 THE EXISTENCE OF HARMONIC MAPS IN TWO DIMENSIONS 509
9.3 REGULARITY RESULTS 530
EXERCISES FOR CHAPTER 9 544
10 VARIATIONAL PROBLEMS FROM QUANTUM FIELD THEORY 547
10.1 THE GINZBURG-LANDAU FUNCTIONAL 547
10.2 THE SEIBERG-WITTEN FUNCTIONAL 555
10.3 DIRAC-HARMONIC MAPS 562
EXERCISES FOR CHAPTER 10 569
A LINEAR ELLIPTIC PARTIAL DIFFERENTIAL EQUATIONS 571
A.I SOBOLEV SPACES 571
A.2 LINEAR ELLIPTIC EQUATIONS 576
A.3 LINEAR PARABOLIC EQUATIONS 580
B FUNDAMENTAL GROUPS AND COVERING SPACES 583
BIBLIOGRAPHY 587
INDEX 605
|
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| author | Jost, Jürgen 1956- |
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| callnumber-raw | QA649 |
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| callnumber-subject | QA - Mathematics |
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| classification_tum | MAT 537f |
| ctrlnum | (OCoLC)748699646 (DE-599)BVBBV039527115 |
| dewey-full | 516.3/73 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 516 - Geometry |
| dewey-raw | 516.3/73 |
| dewey-search | 516.3/73 |
| dewey-sort | 3516.3 273 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| edition | 6. ed. |
| format | Book |
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| illustrated | Illustrated |
| indexdate | 2024-07-10T00:05:32Z |
| institution | BVB |
| isbn | 9783642212970 |
| language | English |
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| physical | XIII, 611 S. graph. Darst. |
| publishDate | 2011 |
| publishDateSearch | 2011 |
| publishDateSort | 2011 |
| publisher | Springer |
| record_format | marc |
| series2 | Universitext |
| spelling | Jost, Jürgen 1956- Verfasser (DE-588)115774564 aut Riemannian geometry and geometric analysis Jürgen Jost 6. ed. Berlin [u.a.] Springer 2011 XIII, 611 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Universitext Geometry, Riemannian Riemannsche Geometrie (DE-588)4128462-8 gnd rswk-swf Geometrische Analysis (DE-588)4156708-0 gnd rswk-swf Riemannsche Geometrie (DE-588)4128462-8 s Geometrische Analysis (DE-588)4156708-0 s 1\p DE-604 DE-604 DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=024379472&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Jost, Jürgen 1956- Riemannian geometry and geometric analysis Geometry, Riemannian Riemannsche Geometrie (DE-588)4128462-8 gnd Geometrische Analysis (DE-588)4156708-0 gnd |
| subject_GND | (DE-588)4128462-8 (DE-588)4156708-0 |
| title | Riemannian geometry and geometric analysis |
| title_auth | Riemannian geometry and geometric analysis |
| title_exact_search | Riemannian geometry and geometric analysis |
| title_full | Riemannian geometry and geometric analysis Jürgen Jost |
| title_fullStr | Riemannian geometry and geometric analysis Jürgen Jost |
| title_full_unstemmed | Riemannian geometry and geometric analysis Jürgen Jost |
| title_short | Riemannian geometry and geometric analysis |
| title_sort | riemannian geometry and geometric analysis |
| topic | Geometry, Riemannian Riemannsche Geometrie (DE-588)4128462-8 gnd Geometrische Analysis (DE-588)4156708-0 gnd |
| topic_facet | Geometry, Riemannian Riemannsche Geometrie Geometrische Analysis |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=024379472&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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