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Author : Rolf Schneider
Release : 1993-02-25
Genre : Mathematics
Kind : eBook
Book Rating : 207/5 ( reviews)
Book Synopsis Convex Bodies by : Rolf Schneider
Download or read book Convex Bodies written by Rolf Schneider. This book was released on 1993-02-25. Available in PDF, EPUB and Kindle. Book excerpt: A comprehensive introduction to convex bodies giving full proofs for some deeper theorems which have never previously been brought together.
Author : Rolf Schneider
Release : 2013-10-31
Genre : Mathematics
Kind : eBook
Book Rating : 613/5 ( reviews)
Book Synopsis Convex Bodies: The Brunn–Minkowski Theory by : Rolf Schneider
Download or read book Convex Bodies: The Brunn–Minkowski Theory written by Rolf Schneider. This book was released on 2013-10-31. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Author : Tommy Bonnesen
Release : 1987
Genre : Mathematics
Kind : eBook
Book Rating : /5 ( reviews)
Book Synopsis Theory of Convex Bodies by : Tommy Bonnesen
Download or read book Theory of Convex Bodies written by Tommy Bonnesen. This book was released on 1987. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Rolf Schneider
Release : 2014
Genre : Mathematics
Kind : eBook
Book Rating : 010/5 ( reviews)
Book Synopsis Convex Bodies: The Brunn–Minkowski Theory by : Rolf Schneider
Download or read book Convex Bodies: The Brunn–Minkowski Theory written by Rolf Schneider. This book was released on 2014. Available in PDF, EPUB and Kindle. Book excerpt: A complete presentation of a central part of convex geometry, from basics for beginners, to the exposition of current research.
Author : Silouanos Brazitikos
Release : 2014-04-24
Genre : Mathematics
Kind : eBook
Book Rating : 562/5 ( reviews)
Book Synopsis Geometry of Isotropic Convex Bodies by : Silouanos Brazitikos
Download or read book Geometry of Isotropic Convex Bodies written by Silouanos Brazitikos. This book was released on 2014-04-24. Available in PDF, EPUB and Kindle. Book excerpt: The study of high-dimensional convex bodies from a geometric and analytic point of view, with an emphasis on the dependence of various parameters on the dimension stands at the intersection of classical convex geometry and the local theory of Banach spaces. It is also closely linked to many other fields, such as probability theory, partial differential equations, Riemannian geometry, harmonic analysis and combinatorics. It is now understood that the convexity assumption forces most of the volume of a high-dimensional convex body to be concentrated in some canonical way and the main question is whether, under some natural normalization, the answer to many fundamental questions should be independent of the dimension. The aim of this book is to introduce a number of well-known questions regarding the distribution of volume in high-dimensional convex bodies, which are exactly of this nature: among them are the slicing problem, the thin shell conjecture and the Kannan-Lovász-Simonovits conjecture. This book provides a self-contained and up to date account of the progress that has been made in the last fifteen years.
