Convex Bodies

The Brunn-Minkowski Theory

Author: Rolf Schneider

Publisher: Cambridge University Press

ISBN: 9780521352208

Category: Mathematics

Page: 490

View: 1103

DOWNLOAD NOW »
A comprehensive introduction to convex bodies giving full proofs for some deeper theorems which have never previously been brought together.

Convex Bodies: The Brunn–Minkowski Theory

Author: Rolf Schneider

Publisher: Cambridge University Press

ISBN: 1107601010

Category: Mathematics

Page: 760

View: 8437

DOWNLOAD NOW »
A complete presentation of a central part of convex geometry, from basics for beginners, to the exposition of current research.

Geometry of Isotropic Convex Bodies

Author: Silouanos Brazitikos,Apostolos Giannopoulos,Petros Valettas,Beatrice-Helen Vritsiou

Publisher: American Mathematical Soc.

ISBN: 1470414562

Category: Mathematics

Page: 594

View: 7411

DOWNLOAD NOW »
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.

Convexity and Concentration

Author: Eric Carlen,Mokshay Madiman,Elisabeth M. Werner

Publisher: Springer

ISBN: 1493970054

Category: Mathematics

Page: 626

View: 7638

DOWNLOAD NOW »
This volume presents some of the research topics discussed at the 2014-2015 Annual Thematic Program Discrete Structures: Analysis and Applications at the Institute of Mathematics and its Applications during the Spring 2015 where geometric analysis, convex geometry and concentration phenomena were the focus. Leading experts have written surveys of research problems, making state of the art results more conveniently and widely available. The volume is organized into two parts. Part I contains those contributions that focus primarily on problems motivated by probability theory, while Part II contains those contributions that focus primarily on problems motivated by convex geometry and geometric analysis. This book will be of use to those who research convex geometry, geometric analysis and probability directly or apply such methods in other fields.

Algebraic and Geometric Combinatorics

Euroconference in Mathematics : Algebraic and Geometric Combinatorics, August 20-26, 2005, Anogia, Crete, Greece

Author: Christos A. Athanasiadis

Publisher: American Mathematical Soc.

ISBN: 0821840800

Category: Mathematics

Page: 324

View: 4659

DOWNLOAD NOW »
This volume contains original research and survey articles stemming from the Euroconference ""Algebraic and Geometric Combinatorics"". The papers discuss a wide range of problems that illustrate interactions of combinatorics with other branches of mathematics, such as commutative algebra, algebraic geometry, convex and discrete geometry, enumerative geometry, and topology of complexes and partially ordered sets. Among the topics covered are combinatorics of polytopes, lattice polytopes, triangulations and subdivisions, Cohen-Macaulay cell complexes, monomial ideals, geometry of toric surfaces, groupoids in combinatorics, Kazhdan-Lusztig combinatorics, and graph colorings. This book is aimed at researchers and graduate students interested in various aspects of modern combinatorial theories.

Tensor Valuations and Their Applications in Stochastic Geometry and Imaging

Author: Eva B. Vedel Jensen,Markus Kiderlen

Publisher: Springer

ISBN: 3319519514

Category: Mathematics

Page: 462

View: 4970

DOWNLOAD NOW »
The purpose of this volume is to give an up-to-date introduction to tensor valuations and their applications. Starting with classical results concerning scalar-valued valuations on the families of convex bodies and convex polytopes, it proceeds to the modern theory of tensor valuations. Product and Fourier-type transforms are introduced and various integral formulae are derived. New and well-known results are presented, together with generalizations in several directions, including extensions to the non-Euclidean setting and to non-convex sets. A variety of applications of tensor valuations to models in stochastic geometry, to local stereology and to imaging are also discussed.

Concentration, Functional Inequalities, and Isoperimetry

International Workshop on Concentration, Functional Inequalities, and Isoperimetry, October 29-November 1, 2009, Florida Atlantic University, Boca Raton, Florida

Author: Christian Houdré

Publisher: American Mathematical Soc.

ISBN: 0821849719

Category: Mathematics

Page: 211

View: 3819

DOWNLOAD NOW »
The volume contains the proceedings of the international workshop on Concentration, Functional Inequalities and Isoperimetry, held at Florida Atlantic University in Boca Raton, Florida, from October 29-November 1, 2009. The interactions between concentration, isoperimetry and functional inequalities have led to many significant advances in functional analysis and probability theory. Important progress has also taken place in combinatorics, geometry, harmonic analysis and mathematical physics, to name but a few fields, with recent new applications in random matrices and information theory. This book should appeal to graduate students and researchers interested in the fascinating interplay between analysis, probability, and geometry.

Convex Polyhedra

Author: A.D. Alexandrov

Publisher: Springer Science & Business Media

ISBN: 3540263403

Category: Mathematics

Page: 542

View: 4791

DOWNLOAD NOW »
This classic geometry text explores the theory of 3-dimensional convex polyhedra in a unique fashion, with exceptional detail. Vital and clearly written, the book includes the basics of convex polyhedra and collects the most general existence theorems for convex polyhedra that are proved by a new and unified method. This edition includes a comprehensive bibliography by V.A. Zalgaller, and related papers as supplements to the original text.