Geometry Of Isotropic Convex Bodies

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Geometry of Isotropic Convex Bodies

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Author : Silouanos Brazitikos
Publisher : American Mathematical Soc.
ISBN 13 : 1470414562
Total Pages : 594 pages
Book Rating : 4.4/5 (74 download)

Book Synopsis Geometry of Isotropic Convex Bodies by : Silouanos Brazitikos

Download or read book Geometry of Isotropic Convex Bodies written by Silouanos Brazitikos and published by American Mathematical Soc.. This book was released on 2014-04-24 with total page 594 pages. 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.

Fourier Analysis in Convex Geometry

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Author : Alexander Koldobsky
Publisher : American Mathematical Soc.
ISBN 13 : 1470419521
Total Pages : 170 pages
Book Rating : 4.4/5 (74 download)

Book Synopsis Fourier Analysis in Convex Geometry by : Alexander Koldobsky

Download or read book Fourier Analysis in Convex Geometry written by Alexander Koldobsky and published by American Mathematical Soc.. This book was released on 2014-11-12 with total page 170 pages. Available in PDF, EPUB and Kindle. Book excerpt: The study of the geometry of convex bodies based on information about sections and projections of these bodies has important applications in many areas of mathematics and science. In this book, a new Fourier analysis approach is discussed. The idea is to express certain geometric properties of bodies in terms of Fourier analysis and to use harmonic analysis methods to solve geometric problems. One of the results discussed in the book is Ball's theorem, establishing the exact upper bound for the -dimensional volume of hyperplane sections of the -dimensional unit cube (it is for each ). Another is the Busemann-Petty problem: if and are two convex origin-symmetric -dimensional bodies and the -dimensional volume of each central hyperplane section of is less than the -dimensional volume of the corresponding section of , is it true that the -dimensional volume of is less than the volume of ? (The answer is positive for and negative for .) The book is suitable for graduate students and researchers interested in geometry, harmonic and functional analysis, and probability. Prerequisites for reading this book include basic real, complex, and functional analysis.

Selected Topics in Convex Geometry

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Author : Maria Moszynska
Publisher : Springer Science & Business Media
ISBN 13 : 0817644512
Total Pages : 226 pages
Book Rating : 4.8/5 (176 download)

Book Synopsis Selected Topics in Convex Geometry by : Maria Moszynska

Download or read book Selected Topics in Convex Geometry written by Maria Moszynska and published by Springer Science & Business Media. This book was released on 2006-11-24 with total page 226 pages. Available in PDF, EPUB and Kindle. Book excerpt: Examines in detail those topics in convex geometry that are concerned with Euclidean space Enriched by numerous examples, illustrations, and exercises, with a good bibliography and index Requires only a basic knowledge of geometry, linear algebra, analysis, topology, and measure theory Can be used for graduates courses or seminars in convex geometry, geometric and convex combinatorics, and convex analysis and optimization

The Interface Between Convex Geometry and Harmonic Analysis

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Author : Alexander Koldobsky
Publisher : American Mathematical Soc.
ISBN 13 : 9780821883358
Total Pages : 128 pages
Book Rating : 4.8/5 (833 download)

Book Synopsis The Interface Between Convex Geometry and Harmonic Analysis by : Alexander Koldobsky

Download or read book The Interface Between Convex Geometry and Harmonic Analysis written by Alexander Koldobsky and published by American Mathematical Soc.. This book was released on with total page 128 pages. Available in PDF, EPUB and Kindle. Book excerpt: "The book is written in the form of lectures accessible to graduate students. This approach allows the reader to clearly see the main ideas behind the method, rather than to dwell on technical difficulties. The book also contains discussions of the most recent advances in the subject. The first section of each lecture is a snapshot of that lecture. By reading each of these sections first, novices can gain an overview of the subject, then return to the full text for more details."--BOOK JACKET.

Affine Geometry of Convex Bodies

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Author : Kurt Leichtweiß
Publisher : Wiley-VCH
ISBN 13 : 9783527402618
Total Pages : 0 pages
Book Rating : 4.4/5 (26 download)

Book Synopsis Affine Geometry of Convex Bodies by : Kurt Leichtweiß

Download or read book Affine Geometry of Convex Bodies written by Kurt Leichtweiß and published by Wiley-VCH. This book was released on 1999-01-12 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: The theory of convex bodies is nowadays an important independent topic of geometry. The author discusses the equiaffine geometry and differential geometry of convex bodies and convex surfaces and especially stresses analogies to classical Euclidean differential geometry. These theories are illustrated by practical applications in areas such as shipbuilding. He offers an accessible introduction to the latest developments in the subject.

Theory of Convex Bodies

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Author : Tommy Bonnesen
Publisher :
ISBN 13 :
Total Pages : 192 pages
Book Rating : 4.3/5 (91 download)

Book Synopsis Theory of Convex Bodies by : Tommy Bonnesen

Download or read book Theory of Convex Bodies written by Tommy Bonnesen and published by . This book was released on 1987 with total page 192 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Affine Geometry of Convex Bodies

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Author : K. Leichtweiss
Publisher :
ISBN 13 : 9783335005148
Total Pages : 310 pages
Book Rating : 4.0/5 (51 download)

Book Synopsis Affine Geometry of Convex Bodies by : K. Leichtweiss

Download or read book Affine Geometry of Convex Bodies written by K. Leichtweiss and published by . This book was released on 1998-01-01 with total page 310 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Convex Bodies: The Brunn–Minkowski Theory

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Author : Rolf Schneider
Publisher : Cambridge University Press
ISBN 13 : 1107601010
Total Pages : 759 pages
Book Rating : 4.1/5 (76 download)

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 and published by Cambridge University Press. This book was released on 2014 with total page 759 pages. 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.

Asymptotic Geometric Analysis, Part II

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Author : Shiri Artstein-Avidan
Publisher : American Mathematical Society
ISBN 13 : 1470463601
Total Pages : 645 pages
Book Rating : 4.4/5 (74 download)

Book Synopsis Asymptotic Geometric Analysis, Part II by : Shiri Artstein-Avidan

Download or read book Asymptotic Geometric Analysis, Part II written by Shiri Artstein-Avidan and published by American Mathematical Society. This book was released on 2021-12-13 with total page 645 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is a continuation of Asymptotic Geometric Analysis, Part I, which was published as volume 202 in this series. Asymptotic geometric analysis studies properties of geometric objects, such as normed spaces, convex bodies, or convex functions, when the dimensions of these objects increase to infinity. The asymptotic approach reveals many very novel phenomena which influence other fields in mathematics, especially where a large data set is of main concern, or a number of parameters which becomes uncontrollably large. One of the important features of this new theory is in developing tools which allow studying high parametric families. Among the topics covered in the book are measure concentration, isoperimetric constants of log-concave measures, thin-shell estimates, stochastic localization, the geometry of Gaussian measures, volume inequalities for convex bodies, local theory of Banach spaces, type and cotype, the Banach-Mazur compactum, symmetrizations, restricted invertibility, and functional versions of geometric notions and inequalities.

Convex Geometric Analysis

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Author : Keith M. Ball
Publisher : Cambridge University Press
ISBN 13 : 9780521642590
Total Pages : 260 pages
Book Rating : 4.6/5 (425 download)

Book Synopsis Convex Geometric Analysis by : Keith M. Ball

Download or read book Convex Geometric Analysis written by Keith M. Ball and published by Cambridge University Press. This book was released on 1999-01-28 with total page 260 pages. Available in PDF, EPUB and Kindle. Book excerpt: Articles on classical convex geometry, geometric functional analysis, computational geometry, and related areas of harmonic analysis, first published in 1999.

Bodies of Constant Width

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Author : Horst Martini
Publisher : Springer
ISBN 13 : 3030038688
Total Pages : 486 pages
Book Rating : 4.0/5 (3 download)

Book Synopsis Bodies of Constant Width by : Horst Martini

Download or read book Bodies of Constant Width written by Horst Martini and published by Springer. This book was released on 2019-03-16 with total page 486 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the first comprehensive monograph to thoroughly investigate constant width bodies, which is a classic area of interest within convex geometry. It examines bodies of constant width from several points of view, and, in doing so, shows surprising connections between various areas of mathematics. Concise explanations and detailed proofs demonstrate the many interesting properties and applications of these bodies. Numerous instructive diagrams are provided throughout to illustrate these concepts. An introduction to convexity theory is first provided, and the basic properties of constant width bodies are then presented. The book then delves into a number of related topics, which include Constant width bodies in convexity (sections and projections, complete and reduced sets, mixed volumes, and further partial fields) Sets of constant width in non-Euclidean geometries (in real Banach spaces, and in hyperbolic, spherical, and further non-Euclidean spaces) The concept of constant width in analysis (using Fourier series, spherical integration, and other related methods) Sets of constant width in differential geometry (using systems of lines and discussing notions like curvature, evolutes, etc.) Bodies of constant width in topology (hyperspaces, transnormal manifolds, fiber bundles, and related topics) The notion of constant width in discrete geometry (referring to geometric inequalities, packings and coverings, etc.) Technical applications, such as film projectors, the square-hole drill, and rotary engines Bodies of Constant Width: An Introduction to Convex Geometry with Applications will be a valuable resource for graduate and advanced undergraduate students studying convex geometry and related fields. Additionally, it will appeal to any mathematicians with a general interest in geometry.

Geometric Aspects of Functional Analysis

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Author : Bo'az Klartag
Publisher : Springer
ISBN 13 : 3319094777
Total Pages : 463 pages
Book Rating : 4.3/5 (19 download)

Book Synopsis Geometric Aspects of Functional Analysis by : Bo'az Klartag

Download or read book Geometric Aspects of Functional Analysis written by Bo'az Klartag and published by Springer. This book was released on 2014-10-08 with total page 463 pages. Available in PDF, EPUB and Kindle. Book excerpt: As in the previous Seminar Notes, the current volume reflects general trends in the study of Geometric Aspects of Functional Analysis. Most of the papers deal with different aspects of Asymptotic Geometric Analysis, understood in a broad sense; many continue the study of geometric and volumetric properties of convex bodies and log-concave measures in high-dimensions and in particular the mean-norm, mean-width, metric entropy, spectral-gap, thin-shell and slicing parameters, with applications to Dvoretzky and Central-Limit-type results. The study of spectral properties of various systems, matrices, operators and potentials is another central theme in this volume. As expected, probabilistic tools play a significant role and probabilistic questions regarding Gaussian noise stability, the Gaussian Free Field and First Passage Percolation are also addressed. The historical connection to the field of Classical Convexity is also well represented with new properties and applications of mixed-volumes. The interplay between the real convex and complex pluri-subharmonic settings continues to manifest itself in several additional articles. All contributions are original research papers and were subject to the usual refereeing standards.

Approaching the Kannan-Lovász-Simonovits and Variance Conjectures

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Author : David Alonso-Gutiérrez
Publisher : Springer
ISBN 13 : 3319132636
Total Pages : 148 pages
Book Rating : 4.3/5 (191 download)

Book Synopsis Approaching the Kannan-Lovász-Simonovits and Variance Conjectures by : David Alonso-Gutiérrez

Download or read book Approaching the Kannan-Lovász-Simonovits and Variance Conjectures written by David Alonso-Gutiérrez and published by Springer. This book was released on 2015-01-07 with total page 148 pages. Available in PDF, EPUB and Kindle. Book excerpt: Focusing on two central conjectures of Asymptotic Geometric Analysis, the Kannan-Lovász-Simonovits spectral gap conjecture and the variance conjecture, these Lecture Notes present the theory in an accessible way, so that interested readers, even those who are not experts in the field, will be able to appreciate the treated topics. Offering a presentation suitable for professionals with little background in analysis, geometry or probability, the work goes directly to the connection between isoperimetric-type inequalities and functional inequalities, giving the interested reader rapid access to the core of these conjectures. In addition, four recent and important results in this theory are presented in a compelling way. The first two are theorems due to Eldan-Klartag and Ball-Nguyen, relating the variance and the KLS conjectures, respectively, to the hyperplane conjecture. Next, the main ideas needed prove the best known estimate for the thin-shell width given by Guédon-Milman and an approach to Eldan's work on the connection between the thin-shell width and the KLS conjecture are detailed.

High-Dimensional Probability

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Author : Roman Vershynin
Publisher : Cambridge University Press
ISBN 13 : 1108415199
Total Pages : 299 pages
Book Rating : 4.1/5 (84 download)

Book Synopsis High-Dimensional Probability by : Roman Vershynin

Download or read book High-Dimensional Probability written by Roman Vershynin and published by Cambridge University Press. This book was released on 2018-09-27 with total page 299 pages. Available in PDF, EPUB and Kindle. Book excerpt: An integrated package of powerful probabilistic tools and key applications in modern mathematical data science.

Geometric Aspects of Harmonic Analysis

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Author : Paolo Ciatti
Publisher : Springer Nature
ISBN 13 : 3030720586
Total Pages : 488 pages
Book Rating : 4.0/5 (37 download)

Book Synopsis Geometric Aspects of Harmonic Analysis by : Paolo Ciatti

Download or read book Geometric Aspects of Harmonic Analysis written by Paolo Ciatti and published by Springer Nature. This book was released on 2021-09-27 with total page 488 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume originated in talks given in Cortona at the conference "Geometric aspects of harmonic analysis" held in honor of the 70th birthday of Fulvio Ricci. It presents timely syntheses of several major fields of mathematics as well as original research articles contributed by some of the finest mathematicians working in these areas. The subjects dealt with are topics of current interest in closely interrelated areas of Fourier analysis, singular integral operators, oscillatory integral operators, partial differential equations, multilinear harmonic analysis, and several complex variables. The work is addressed to researchers in the field.

Discrete Geometry

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Author : Andras Bezdek
Publisher : CRC Press
ISBN 13 : 9780203911211
Total Pages : 492 pages
Book Rating : 4.9/5 (112 download)

Book Synopsis Discrete Geometry by : Andras Bezdek

Download or read book Discrete Geometry written by Andras Bezdek and published by CRC Press. This book was released on 2003-02-04 with total page 492 pages. Available in PDF, EPUB and Kindle. Book excerpt: Celebrating the work of Professor W. Kuperberg, this reference explores packing and covering theory, tilings, combinatorial and computational geometry, and convexity, featuring an extensive collection of problems compiled at the Discrete Geometry Special Session of the American Mathematical Society in New Orleans, Louisiana. Discrete Geometry analy

Partitions of Mass-distributions and of Convex Bodies by Hyperplanes

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Author : B. Grunbaum
Publisher :
ISBN 13 :
Total Pages : 12 pages
Book Rating : 4.3/5 (91 download)

Book Synopsis Partitions of Mass-distributions and of Convex Bodies by Hyperplanes by : B. Grunbaum

Download or read book Partitions of Mass-distributions and of Convex Bodies by Hyperplanes written by B. Grunbaum and published by . This book was released on 1960 with total page 12 pages. Available in PDF, EPUB and Kindle. Book excerpt: