Convex Bodies

The Brunn-Minkowski Theory

Author: Rolf Schneider

Publisher: Cambridge University Press

ISBN: 9780521352208

Category: Mathematics

Page: 490

View: 9127

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

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: 1825

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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: 7709

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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.

Convex Bodies: The Brunn–Minkowski Theory

Author: Rolf Schneider

Publisher: Cambridge University Press

ISBN: 1107601010

Category: Mathematics

Page: 760

View: 2008

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

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: 1582

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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.

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

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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.

Convex Polyhedra

Author: A.D. Alexandrov

Publisher: Springer Science & Business Media

ISBN: 3540263403

Category: Mathematics

Page: 542

View: 2700

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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.

European Congress of Mathematics

Barcelona, July 10-14, 2000

Author: Carlos Casacuberta

Publisher: Birkhauser

ISBN: N.A

Category: Mathematics

Page: 641

View: 8996

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This is the second volume of the proceedings of the third European Congress of Mathematics. Volume I presents the speeches delivered at the Congress, the list of lectures, and short summaries of the achievements of the prize winners as well as papers by plenary and parallel speakers. The second volume collects articles by prize winners and speakers of the mini-symposia.This two-volume set thus gives an overview of the state of the art in many fields of mathematics and is therefore of interest to every professional mathematician.

Stochastic Geometry

Lectures Given at the C.I.M.E. Summer School Held in Martina Franca, Italy, September 13-18, 2004

Author: A. Baddeley,W. Weil

Publisher: Springer Verlag

ISBN: N.A

Category: Mathematics

Page: 284

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Stochastic Geometry is the mathematical discipline which studies mathematical models for random geometric structures, as they appear frequently in almost all natural sciences or technical fields. Although its roots can be traced back to the 18th century (the Buffon needle problem), the modern theory of random sets was founded by D. Kendall and G. Matheron in the early 1970's. Its rapid development was influenced by applications in Spatial Statistics and by its close connections to Integral Geometry. The volume "Stochastic Geometry" contains the lectures given at the CIME summer school in Martina Franca in September 2004. The four main lecturers covered the areas of Spatial Statistics, Random Points, Integral Geometry and Random Sets, they are complemented by two additional contributions on Random Mosaics and Crystallization Processes. The book presents an up-to-date description of important parts of Stochastic Geometry.

Convex and fractal geometry

Author: Robert J. MacG. Dawson

Publisher: N.A

ISBN: N.A

Category: Convex geometry

Page: 222

View: 7179

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The conference Convex and Fractal Geometry was held at the Stefan Banach International Mathematical Center at Bedlewo, May 21-26, 2007. ... This volume contains twelve papers related to the talks delivered at that conference.