Cambridge University Press eBooks· 2013
Convex Bodies The Brunn-MinkowskiTheory
- 957citations
- 2013year
Short summary
This monograph offers a comprehensive introduction to convex bodies, focusing on the Brunn-Minkowski theory and its applications to volume and surface area. The second edition significantly expands on recent developments, including new chapters on valuations, Lp Brunn-Minkowski theory, and affine constructions.
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Key points
- Focuses on the Brunn-Minkowski theory for studying convex bodies.
- Explains concepts like mixed volume and fundamental inequalities.
- Second edition includes new chapters on valuations, Lp theory, and affine constructions.
- Provides full proofs for key theorems and an extensive reference list.
AI-generated from the title and abstract; the full text is not read.
Abstract
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.
The authors' abstract, as published at the source. Cambridge University Press eBooks, 2013 · DOI ↗
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Field: Applied Mathematics
Applied MathematicsMathematics