The geometry of total curvature on complete open surfaces:
This is a self-contained account of how some modern ideas in differential geometry can be used to tackle and extend classical results in integral geometry. The authors investigate the influence of total curvature on the metric structure of complete, non-compact Riemannian 2-manifolds, though their w...
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| Main Author: | |
|---|---|
| Format: | Electronic eBook |
| Language: | English |
| Published: |
Cambridge
Cambridge University Press
2003
|
| Series: | Cambridge tracts in mathematics
159 |
| Subjects: | |
| Online Access: | BSB01 FHN01 UBR01 Volltext |
| Summary: | This is a self-contained account of how some modern ideas in differential geometry can be used to tackle and extend classical results in integral geometry. The authors investigate the influence of total curvature on the metric structure of complete, non-compact Riemannian 2-manifolds, though their work, much of which has never appeared in book form before, can be extended to more general spaces. Many classical results are introduced and then extended by the authors. The compactification of complete open surfaces is discussed, as are Busemann functions for rays. Open problems are provided in each chapter, and the text is richly illustrated with figures designed to help the reader understand the subject matter and get intuitive ideas about the subject. The treatment is self-contained, assuming only a basic knowledge of manifold theory, so is suitable for graduate students and non-specialists who seek an introduction to this modern area of differential geometry |
| Physical Description: | 1 Online-Ressource (ix, 284 Seiten) |
| ISBN: | 9780511543159 |
| DOI: | 10.1017/CBO9780511543159 |
Staff View
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| 245 | 1 | 0 | |a The geometry of total curvature on complete open surfaces |c Katsuhiro Shiohama, Takashi Shioya, Minoru Tanaka |
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| 505 | 8 | |a 1. Riemannian geometry -- 2. The classical results of Cohn-Vossen and Huber -- 3. The ideal boundary -- 4. The cut loci of complete open surfaces -- 5. Isoperimetric inequalities -- 6. Mass of rays. -- 7. The poles and cut loci of a surface of revolution -- 8. The behavior of geodesics | |
| 520 | |a This is a self-contained account of how some modern ideas in differential geometry can be used to tackle and extend classical results in integral geometry. The authors investigate the influence of total curvature on the metric structure of complete, non-compact Riemannian 2-manifolds, though their work, much of which has never appeared in book form before, can be extended to more general spaces. Many classical results are introduced and then extended by the authors. The compactification of complete open surfaces is discussed, as are Busemann functions for rays. Open problems are provided in each chapter, and the text is richly illustrated with figures designed to help the reader understand the subject matter and get intuitive ideas about the subject. The treatment is self-contained, assuming only a basic knowledge of manifold theory, so is suitable for graduate students and non-specialists who seek an introduction to this modern area of differential geometry | ||
| 650 | 4 | |a Riemannian manifolds | |
| 650 | 4 | |a Curves on surfaces | |
| 650 | 4 | |a Global differential geometry | |
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| author | Shiohama, Katsuhiro 1940- |
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| contents | 1. Riemannian geometry -- 2. The classical results of Cohn-Vossen and Huber -- 3. The ideal boundary -- 4. The cut loci of complete open surfaces -- 5. Isoperimetric inequalities -- 6. Mass of rays. -- 7. The poles and cut loci of a surface of revolution -- 8. The behavior of geodesics |
| ctrlnum | (ZDB-20-CBO)CR9780511543159 (OCoLC)850372113 (DE-599)BVBBV043942124 |
| dewey-full | 516.3/52 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 516 - Geometry |
| dewey-raw | 516.3/52 |
| dewey-search | 516.3/52 |
| dewey-sort | 3516.3 252 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| doi_str_mv | 10.1017/CBO9780511543159 |
| format | Electronic eBook |
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| id | DE-604.BV043942124 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T07:39:17Z |
| institution | BVB |
| isbn | 9780511543159 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-029351094 |
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| physical | 1 Online-Ressource (ix, 284 Seiten) |
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| publishDate | 2003 |
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| publisher | Cambridge University Press |
| record_format | marc |
| series2 | Cambridge tracts in mathematics |
| spelling | Shiohama, Katsuhiro 1940- Verfasser (DE-588)1055767916 aut The geometry of total curvature on complete open surfaces Katsuhiro Shiohama, Takashi Shioya, Minoru Tanaka Cambridge Cambridge University Press 2003 1 Online-Ressource (ix, 284 Seiten) txt rdacontent c rdamedia cr rdacarrier Cambridge tracts in mathematics 159 1. Riemannian geometry -- 2. The classical results of Cohn-Vossen and Huber -- 3. The ideal boundary -- 4. The cut loci of complete open surfaces -- 5. Isoperimetric inequalities -- 6. Mass of rays. -- 7. The poles and cut loci of a surface of revolution -- 8. The behavior of geodesics This is a self-contained account of how some modern ideas in differential geometry can be used to tackle and extend classical results in integral geometry. The authors investigate the influence of total curvature on the metric structure of complete, non-compact Riemannian 2-manifolds, though their work, much of which has never appeared in book form before, can be extended to more general spaces. Many classical results are introduced and then extended by the authors. The compactification of complete open surfaces is discussed, as are Busemann functions for rays. Open problems are provided in each chapter, and the text is richly illustrated with figures designed to help the reader understand the subject matter and get intuitive ideas about the subject. The treatment is self-contained, assuming only a basic knowledge of manifold theory, so is suitable for graduate students and non-specialists who seek an introduction to this modern area of differential geometry Riemannian manifolds Curves on surfaces Global differential geometry Ebene Kurve (DE-588)4150970-5 gnd rswk-swf Riemannscher Raum (DE-588)4128295-4 gnd rswk-swf Globale Differentialgeometrie (DE-588)4021286-5 gnd rswk-swf Riemannscher Raum (DE-588)4128295-4 s Ebene Kurve (DE-588)4150970-5 s Globale Differentialgeometrie (DE-588)4021286-5 s DE-604 Shioya, Takashi 1963- Sonstige (DE-588)108210132X oth Tanaka, Minoru 1949- Sonstige oth Erscheint auch als Druck-Ausgabe 978-0-521-45054-6 https://doi.org/10.1017/CBO9780511543159 Verlag URL des Erstveröffentlichers Volltext |
| spellingShingle | Shiohama, Katsuhiro 1940- The geometry of total curvature on complete open surfaces 1. Riemannian geometry -- 2. The classical results of Cohn-Vossen and Huber -- 3. The ideal boundary -- 4. The cut loci of complete open surfaces -- 5. Isoperimetric inequalities -- 6. Mass of rays. -- 7. The poles and cut loci of a surface of revolution -- 8. The behavior of geodesics Riemannian manifolds Curves on surfaces Global differential geometry Ebene Kurve (DE-588)4150970-5 gnd Riemannscher Raum (DE-588)4128295-4 gnd Globale Differentialgeometrie (DE-588)4021286-5 gnd |
| subject_GND | (DE-588)4150970-5 (DE-588)4128295-4 (DE-588)4021286-5 |
| title | The geometry of total curvature on complete open surfaces |
| title_auth | The geometry of total curvature on complete open surfaces |
| title_exact_search | The geometry of total curvature on complete open surfaces |
| title_full | The geometry of total curvature on complete open surfaces Katsuhiro Shiohama, Takashi Shioya, Minoru Tanaka |
| title_fullStr | The geometry of total curvature on complete open surfaces Katsuhiro Shiohama, Takashi Shioya, Minoru Tanaka |
| title_full_unstemmed | The geometry of total curvature on complete open surfaces Katsuhiro Shiohama, Takashi Shioya, Minoru Tanaka |
| title_short | The geometry of total curvature on complete open surfaces |
| title_sort | the geometry of total curvature on complete open surfaces |
| topic | Riemannian manifolds Curves on surfaces Global differential geometry Ebene Kurve (DE-588)4150970-5 gnd Riemannscher Raum (DE-588)4128295-4 gnd Globale Differentialgeometrie (DE-588)4021286-5 gnd |
| topic_facet | Riemannian manifolds Curves on surfaces Global differential geometry Ebene Kurve Riemannscher Raum Globale Differentialgeometrie |
| url | https://doi.org/10.1017/CBO9780511543159 |
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