Convex bodies: the Brunn-Minkowski theory
At the heart of this monograph is the Brunn-Minkowski theory, which can be used to great effect in studying such ideas as volume and surface area and their generalizations. In particular, the notions of mixed volume and mixed area measure arise naturally and the fundamental inequalities that are sat...
Gespeichert in:
| Beteilige Person: | |
|---|---|
| Format: | E-Book |
| Sprache: | Englisch |
| Veröffentlicht: |
Cambridge
Cambridge University Press
2014
|
| Ausgabe: | Second edition. |
| Schriftenreihe: | Encyclopedia of mathematics and its applications
volume 151 |
| Links: | https://doi.org/10.1017/CBO9781139003858 |
| Zusammenfassung: | At the heart of this monograph is the Brunn-Minkowski theory, which can be used to great effect in studying such ideas as volume and surface area and their generalizations. In particular, the notions of mixed volume and mixed area measure arise naturally and the fundamental inequalities that are satisfied by mixed volumes are considered here in detail. The author presents a comprehensive introduction to convex bodies, including full proofs for some deeper theorems. The book provides hints and pointers to connections with other fields and an exhaustive reference list. This second edition has been considerably expanded to reflect the rapid developments of the past two decades. It includes new chapters on valuations on convex bodies, on extensions like the Lp Brunn-Minkowski theory, and on affine constructions and inequalities. There are also many supplements and updates to the original chapters, and a substantial expansion of chapter notes and references. |
| Umfang: | 1 Online-Ressource (xxii, 736 Seiten) |
| ISBN: | 9781139003858 |
Internformat
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| 245 | 1 | 0 | |a Convex bodies |b the Brunn-Minkowski theory |c Rolf Schneider, Albert-Ludwigs-Universitat Freiburg, Germany |
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| 490 | 1 | |a Encyclopedia of mathematics and its applications |v volume 151 | |
| 520 | |a At the heart of this monograph is the Brunn-Minkowski theory, which can be used to great effect in studying such ideas as volume and surface area and their generalizations. In particular, the notions of mixed volume and mixed area measure arise naturally and the fundamental inequalities that are satisfied by mixed volumes are considered here in detail. The author presents a comprehensive introduction to convex bodies, including full proofs for some deeper theorems. The book provides hints and pointers to connections with other fields and an exhaustive reference list. This second edition has been considerably expanded to reflect the rapid developments of the past two decades. It includes new chapters on valuations on convex bodies, on extensions like the Lp Brunn-Minkowski theory, and on affine constructions and inequalities. There are also many supplements and updates to the original chapters, and a substantial expansion of chapter notes and references. | ||
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| id | ZDB-20-CTM-CR9781139003858 |
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| series2 | Encyclopedia of mathematics and its applications |
| spelling | Schneider, Rolf 1940- Convex bodies the Brunn-Minkowski theory Rolf Schneider, Albert-Ludwigs-Universitat Freiburg, Germany Second edition. Cambridge Cambridge University Press 2014 1 Online-Ressource (xxii, 736 Seiten) txt c cr Encyclopedia of mathematics and its applications volume 151 At the heart of this monograph is the Brunn-Minkowski theory, which can be used to great effect in studying such ideas as volume and surface area and their generalizations. In particular, the notions of mixed volume and mixed area measure arise naturally and the fundamental inequalities that are satisfied by mixed volumes are considered here in detail. The author presents a comprehensive introduction to convex bodies, including full proofs for some deeper theorems. The book provides hints and pointers to connections with other fields and an exhaustive reference list. This second edition has been considerably expanded to reflect the rapid developments of the past two decades. It includes new chapters on valuations on convex bodies, on extensions like the Lp Brunn-Minkowski theory, and on affine constructions and inequalities. There are also many supplements and updates to the original chapters, and a substantial expansion of chapter notes and references. Erscheint auch als Druck-Ausgabe 9781107601017 |
| spellingShingle | Schneider, Rolf 1940- Convex bodies the Brunn-Minkowski theory |
| title | Convex bodies the Brunn-Minkowski theory |
| title_auth | Convex bodies the Brunn-Minkowski theory |
| title_exact_search | Convex bodies the Brunn-Minkowski theory |
| title_full | Convex bodies the Brunn-Minkowski theory Rolf Schneider, Albert-Ludwigs-Universitat Freiburg, Germany |
| title_fullStr | Convex bodies the Brunn-Minkowski theory Rolf Schneider, Albert-Ludwigs-Universitat Freiburg, Germany |
| title_full_unstemmed | Convex bodies the Brunn-Minkowski theory Rolf Schneider, Albert-Ludwigs-Universitat Freiburg, Germany |
| title_short | Convex bodies |
| title_sort | convex bodies the brunn minkowski theory |
| title_sub | the Brunn-Minkowski theory |
| work_keys_str_mv | AT schneiderrolf convexbodiesthebrunnminkowskitheory |