A course in metric geometry:
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Providence, RI
American Math. Soc.
2001
|
| Series: | Graduate studies in mathematics
33 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XIV, 415 S. |
| ISBN: | 9780821821299 0821821296 |
Staff View
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Record in the Search Index
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| adam_text | Contents
Preface xi
Chapter 1. Metric Spaces 1
§1.1. Definitions 1
§1.2. Examples 3
§1.3. Metrics and Topology 7
§1.4. Lipschitz Maps 9
§1.5. Complete Spaces 10
§1.6. Compact Spaces 13
§1.7. Hausdorff Measure and Dimension 17
Chapter 2. Length Spaces 25
§2.1. Length Structures 25
§2.2. First Examples of Length Structures 30
§2.3. Length Structures Induced by Metrics 33
§2.4. Characterization of Intrinsic Metrics 38
§2.5. Shortest Paths 43
§2.6. Length and Hausdorff Measure 53
§2.7. Length and Lipschitz Speed 54
Chapter 3. Constructions 59
§3.1. Locality, Gluing and Maximal Metrics 59
§3.2. Polyhedral Spaces 67
§3.3. Isometries and Quotients 75
vii
viii Contents
§3.4. Local Isometries and Coverings 78
§3.5. Arcwise Isometries 86
§3.6. Products and Cones 88
Chapter 4. Spaces of Bounded Curvature 101
§4.1. Definitions 101
§4.2. Examples 109
§4.3. Angles in Alexandrov Spaces and Equivalence of Definitions 114
§4.4. Analysis of Distance Functions 119
§4.5. The First Variation Formula 121
§4.6. Nonzero Curvature Bounds and Globalization 126
§4.7. Curvature of Cones 131
Chapter 5. Smooth Length Structures 135
§5.1. Riemannian Length Structures 136
§5.2. Exponential Map 150
§5.3. Hyperbolic Plane 154
§5.4. Sub Riemannian Metric Structures 178
§5.5. Riemannian and Finsler Volumes 192
§5.6. Besikovitch Inequality 201
Chapter 6. Curvature of Riemannian Metrics 209
§6.1. Motivation: Coordinate Computations 211
§6.2. Covariant Derivative 214
§6.3. Geodesic and Gaussian Curvatures 221
§6.4. Geometric Meaning of Gaussian Curvature 226
§6.5. Comparison Theorems 237
Chapter 7. Space of Metric Spaces 241
§7.1. Examples 242
§7.2. Lipschitz Distance 249
§7.3. Gromov Hausdorff Distance 251
§7.4. Gromov Hausdorff Convergence 260
§7.5. Convergence of Length Spaces 265
Chapter 8. Large scale Geometry 271
§8.1. Noncompact Gromov Hausdorff Limits 271
§8.2. Tangent and Asymptotic Cones 275
Contents ix
§8.3. Quasi isometries 277
§8.4. Gromov Hyperbolic Spaces 284
§8.5. Periodic Metrics 298
Chapter 9. Spaces of Curvature Bounded Above 307
§9.1. Definitions and Local Properties 308
§9.2. Hadamard Spaces 324
§9.3. Fundamental Group of a Nonpositively Curved Space 338
§9.4. Example: Semi dispersing Billiards 341
Chapter 10. Spaces of Curvature Bounded Below 351
§10.1. One More Definition 352
§10.2. Constructions and Examples 354
§10.3. Toponogov s Theorem 360
§10.4. Curvature and Diameter 364
§10.5. Splitting Theorem 366
§10.6. Dimension and Volume 369
§10.7. Gromov Hausdorff Limits 376
§10.8. Local Properties 378
§10.9. Spaces of Directions and Tangent Cones 390
§10.10. Further Information 398
Bibliography 405
Index 409
|
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| language | English |
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| physical | XIV, 415 S. |
| publishDate | 2001 |
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| spelling | Burago, Dmitri Verfasser aut A course in metric geometry Dmitri Burago ; Yuri Burago ; Sergei Ivanov Providence, RI American Math. Soc. 2001 XIV, 415 S. txt rdacontent n rdamedia nc rdacarrier Graduate studies in mathematics 33 Metrische Geometrie Metrischer Raum (DE-588)4169745-5 gnd rswk-swf Metrischer Raum (DE-588)4169745-5 s DE-604 Burago, Jurij D. Verfasser aut Ivanov, Sergej Verfasser aut Erscheint auch als Online-Ausgabe 978-1-4704-1794-9 Graduate studies in mathematics 33 (DE-604)BV009739289 33 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009543097&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Burago, Dmitri Burago, Jurij D. Ivanov, Sergej A course in metric geometry Graduate studies in mathematics Metrische Geometrie Metrischer Raum (DE-588)4169745-5 gnd |
| subject_GND | (DE-588)4169745-5 |
| title | A course in metric geometry |
| title_auth | A course in metric geometry |
| title_exact_search | A course in metric geometry |
| title_full | A course in metric geometry Dmitri Burago ; Yuri Burago ; Sergei Ivanov |
| title_fullStr | A course in metric geometry Dmitri Burago ; Yuri Burago ; Sergei Ivanov |
| title_full_unstemmed | A course in metric geometry Dmitri Burago ; Yuri Burago ; Sergei Ivanov |
| title_short | A course in metric geometry |
| title_sort | a course in metric geometry |
| topic | Metrische Geometrie Metrischer Raum (DE-588)4169745-5 gnd |
| topic_facet | Metrische Geometrie Metrischer Raum |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009543097&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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