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Author: Rolf Schneider
Publisher: Cambridge University Press
Published: 1993-02-25
Total Pages: 506
ISBN-13: 0521352207
DOWNLOAD EBOOK →A comprehensive introduction to convex bodies giving full proofs for some deeper theorems which have never previously been brought together.
Author: Rolf Schneider
Publisher: Cambridge University Press
Published: 2013-10-31
Total Pages: 752
ISBN-13: 1107471613
DOWNLOAD EBOOK →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: Rolf Schneider
Publisher: Cambridge University Press
Published: 2014
Total Pages: 759
ISBN-13: 1107601010
DOWNLOAD EBOOK →A complete presentation of a central part of convex geometry, from basics for beginners, to the exposition of current research.
Author: Daniel Hug
Publisher: Springer Nature
Published: 2020-08-27
Total Pages: 287
ISBN-13: 3030501809
DOWNLOAD EBOOK →This book provides a self-contained introduction to convex geometry in Euclidean space. After covering the basic concepts and results, it develops Brunn–Minkowski theory, with an exposition of mixed volumes, the Brunn–Minkowski inequality, and some of its consequences, including the isoperimetric inequality. Further central topics are then treated, such as surface area measures, projection functions, zonoids, and geometric valuations. Finally, an introduction to integral-geometric formulas in Euclidean space is provided. The numerous exercises and the supplementary material at the end of each section form an essential part of the book. Convexity is an elementary and natural concept. It plays a key role in many mathematical fields, including functional analysis, optimization, probability theory, and stochastic geometry. Paving the way to the more advanced and specialized literature, the material will be accessible to students in the third year and can be covered in one semester.
Author: Silouanos Brazitikos
Publisher: American Mathematical Soc.
Published: 2014-04-24
Total Pages: 618
ISBN-13: 1470414562
DOWNLOAD EBOOK →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.
Author: Gilles Pisier
Publisher: Cambridge University Press
Published: 1999-05-27
Total Pages: 270
ISBN-13: 9780521666350
DOWNLOAD EBOOK →A self-contained presentation of results relating the volume of convex bodies and Banach space geometry.
Author: R.V. Ambartzumian
Publisher: Springer Science & Business Media
Published: 2012-12-06
Total Pages: 135
ISBN-13: 9400939213
DOWNLOAD EBOOK →Author: Herbert Busemann
Publisher: Courier Corporation
Published: 2013-11-07
Total Pages: 210
ISBN-13: 0486154998
DOWNLOAD EBOOK →This exploration of convex surfaces focuses on extrinsic geometry and applications of the Brunn-Minkowski theory. It also examines intrinsic geometry and the realization of intrinsic metrics. 1958 edition.
Author: Richard J. Gardner
Publisher: Cambridge University Press
Published: 2006-06-19
Total Pages: 7
ISBN-13: 0521866804
DOWNLOAD EBOOK →Geometric tomography deals with the retrieval of information about a geometric object from data concerning its projections (shadows) on planes or cross-sections by planes. It is a geometric relative of computerized tomography, which reconstructs an image from X-rays of a human patient. It overlaps with convex geometry, and employs many tools from that area including integral geometry. It also has connections to geometric probing in robotics and to stereology. The main text contains a rigorous treatment of the subject starting from basic concepts and moving up to the research frontier: seventy-two unsolved problems are stated. Each chapter ends with extensive notes, historical remarks, and some biographies. This comprehensive work will be invaluable to specialists in geometry and tomography; the opening chapters can also be read by advanced undergraduate students.
