Handbook Of Convex Geometry

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Handbook of Convex Geometry

Author : Gerard Meurant
Publisher : Elsevier
ISBN 13 : 0080934390
Total Pages : 801 pages
Book Rating : 4.0/5 (89 download)

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Book Synopsis Handbook of Convex Geometry by : Gerard Meurant

Download or read book Handbook of Convex Geometry written by Gerard Meurant and published by Elsevier. This book was released on 2014-06-28 with total page 801 pages. Available in PDF, EPUB and Kindle. Book excerpt: Handbook of Convex Geometry, Volume A offers a survey of convex geometry and its many ramifications and relations with other areas of mathematics, including convexity, geometric inequalities, and convex sets. The selection first offers information on the history of convexity, characterizations of convex sets, and mixed volumes. Topics include elementary convexity, equality in the Aleksandrov-Fenchel inequality, mixed surface area measures, characteristic properties of convex sets in analysis and differential geometry, and extensions of the notion of a convex set. The text then reviews the standard isoperimetric theorem and stability of geometric inequalities. The manuscript takes a look at selected affine isoperimetric inequalities, extremum problems for convex discs and polyhedra, and rigidity. Discussions focus on include infinitesimal and static rigidity related to surfaces, isoperimetric problem for convex polyhedral, bounds for the volume of a convex polyhedron, curvature image inequality, Busemann intersection inequality and its relatives, and Petty projection inequality. The book then tackles geometric algorithms, convexity and discrete optimization, mathematical programming and convex geometry, and the combinatorial aspects of convex polytopes. The selection is a valuable source of data for mathematicians and researchers interested in convex geometry.

Handbook of Convex Geometry

Author : Peter M. Gruber
Publisher : North Holland
ISBN 13 : 9780444895981
Total Pages : 0 pages
Book Rating : 4.8/5 (959 download)

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Book Synopsis Handbook of Convex Geometry by : Peter M. Gruber

Download or read book Handbook of Convex Geometry written by Peter M. Gruber and published by North Holland. This book was released on 2006-02-02 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Handbook of Convex Geometry

Author : P. M. Gruber
Publisher :
ISBN 13 : 9781493305711
Total Pages : 0 pages
Book Rating : 4.3/5 (57 download)

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Book Synopsis Handbook of Convex Geometry by : P. M. Gruber

Download or read book Handbook of Convex Geometry written by P. M. Gruber and published by . This book was released on 1993 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: Handbook of Convex Geometry, Volume B offers a survey of convex geometry and its many ramifications and connections with other fields of mathematics, including convexity, lattices, crystallography, and convex functions.The selection first offers information on the geometry of numbers, lattice points, and packing and covering with convex sets. Discussions focus on packing in non-Euclidean spaces, problems in the Euclidean plane, general convex bodies, computational complexity of lattice point problem, centrally symmetric convex bodies, reduction theory, and lattices and the space of lattices. T

Handbook of Convex Geometry

Author :
Publisher : North Holland
ISBN 13 : 9780444895967
Total Pages : 801 pages
Book Rating : 4.8/5 (959 download)

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Book Synopsis Handbook of Convex Geometry by :

Download or read book Handbook of Convex Geometry written by and published by North Holland. This book was released on 1993-09-07 with total page 801 pages. Available in PDF, EPUB and Kindle. Book excerpt: Handbook of Convex Geometry, Volume A offers a survey of convex geometry and its many ramifications and relations with other areas of mathematics, including convexity, geometric inequalities, and convex sets. The selection first offers information on the history of convexity, characterizations of convex sets, and mixed volumes. Topics include elementary convexity, equality in the Aleksandrov-Fenchel inequality, mixed surface area measures, characteristic properties of convex sets in analysis and differential geometry, and extensions of the notion of a convex set. The text then reviews the standard isoperimetric theorem and stability of geometric inequalities. The manuscript takes a look at selected affine isoperimetric inequalities, extremum problems for convex discs and polyhedra, and rigidity. Discussions focus on include infinitesimal and static rigidity related to surfaces, isoperimetric problem for convex polyhedral, bounds for the volume of a convex polyhedron, curvature image inequality, Busemann intersection inequality and its relatives, and Petty projection inequality. The book then tackles geometric algorithms, convexity and discrete optimization, mathematical programming and convex geometry, and the combinatorial aspects of convex polytopes. The selection is a valuable source of data for mathematicians and researchers interested in convex geometry.

Convex and Discrete Geometry

Author : Peter M. Gruber
Publisher : Springer Science & Business Media
ISBN 13 : 3540711333
Total Pages : 580 pages
Book Rating : 4.5/5 (47 download)

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Book Synopsis Convex and Discrete Geometry by : Peter M. Gruber

Download or read book Convex and Discrete Geometry written by Peter M. Gruber and published by Springer Science & Business Media. This book was released on 2007-05-17 with total page 580 pages. Available in PDF, EPUB and Kindle. Book excerpt: Convex and Discrete Geometry is an area of mathematics situated between analysis, geometry and discrete mathematics with numerous relations to other subdisciplines. This book provides a comprehensive overview of major results, methods and ideas of convex and discrete geometry and its applications. Besides being a graduate-level introduction to the field, it is a practical source of information and orientation for convex geometers, and useful to people working in the applied fields.

Foundations of Convex Geometry

Author : W. A. Coppel
Publisher : Cambridge University Press
ISBN 13 : 9780521639705
Total Pages : 236 pages
Book Rating : 4.6/5 (397 download)

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Book Synopsis Foundations of Convex Geometry by : W. A. Coppel

Download or read book Foundations of Convex Geometry written by W. A. Coppel and published by Cambridge University Press. This book was released on 1998-03-05 with total page 236 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a self-contained and thorough book on the foundations of Euclidean geometry.

Handbook of the Geometry of Banach Spaces

Author :
Publisher : Elsevier
ISBN 13 : 0080532802
Total Pages : 1017 pages
Book Rating : 4.0/5 (85 download)

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Book Synopsis Handbook of the Geometry of Banach Spaces by :

Download or read book Handbook of the Geometry of Banach Spaces written by and published by Elsevier. This book was released on 2001-08-15 with total page 1017 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Handbook presents an overview of most aspects of modernBanach space theory and its applications. The up-to-date surveys, authored by leading research workers in the area, are written to be accessible to a wide audience. In addition to presenting the state of the art of Banach space theory, the surveys discuss the relation of the subject with such areas as harmonic analysis, complex analysis, classical convexity, probability theory, operator theory, combinatorics, logic, geometric measure theory, and partial differential equations. The Handbook begins with a chapter on basic concepts in Banachspace theory which contains all the background needed for reading any other chapter in the Handbook. Each of the twenty one articles in this volume after the basic concepts chapter is devoted to one specific direction of Banach space theory or its applications. Each article contains a motivated introduction as well as an exposition of the main results, methods, and open problems in its specific direction. Most have an extensive bibliography. Many articles contain new proofs of known results as well as expositions of proofs which are hard to locate in the literature or are only outlined in the original research papers. As well as being valuable to experienced researchers in Banach space theory, the Handbook should be an outstanding source for inspiration and information to graduate students and beginning researchers. The Handbook will be useful for mathematicians who want to get an idea of the various developments in Banach space theory.

Bodies of Constant Width

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

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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.

Handbook of Discrete and Computational Geometry

Author : Csaba D. Toth
Publisher : CRC Press
ISBN 13 : 1351645919
Total Pages : 2879 pages
Book Rating : 4.3/5 (516 download)

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Book Synopsis Handbook of Discrete and Computational Geometry by : Csaba D. Toth

Download or read book Handbook of Discrete and Computational Geometry written by Csaba D. Toth and published by CRC Press. This book was released on 2017-11-22 with total page 2879 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Handbook of Discrete and Computational Geometry is intended as a reference book fully accessible to nonspecialists as well as specialists, covering all major aspects of both fields. The book offers the most important results and methods in discrete and computational geometry to those who use them in their work, both in the academic world—as researchers in mathematics and computer science—and in the professional world—as practitioners in fields as diverse as operations research, molecular biology, and robotics. Discrete geometry has contributed significantly to the growth of discrete mathematics in recent years. This has been fueled partly by the advent of powerful computers and by the recent explosion of activity in the relatively young field of computational geometry. This synthesis between discrete and computational geometry lies at the heart of this Handbook. A growing list of application fields includes combinatorial optimization, computer-aided design, computer graphics, crystallography, data analysis, error-correcting codes, geographic information systems, motion planning, operations research, pattern recognition, robotics, solid modeling, and tomography.

Convex Bodies: The Brunn–Minkowski Theory

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

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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.

Handbook of Convex Geometry

Author : Peter M. Gruber
Publisher : North Holland
ISBN 13 :
Total Pages : 774 pages
Book Rating : 4.3/5 (91 download)

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Book Synopsis Handbook of Convex Geometry by : Peter M. Gruber

Download or read book Handbook of Convex Geometry written by Peter M. Gruber and published by North Holland. This book was released on 1993-08-24 with total page 774 pages. Available in PDF, EPUB and Kindle. Book excerpt: Handbook of Convex Geometry, Volume B offers a survey of convex geometry and its many ramifications and connections with other fields of mathematics, including convexity, lattices, crystallography, and convex functions. The selection first offers information on the geometry of numbers, lattice points, and packing and covering with convex sets. Discussions focus on packing in non-Euclidean spaces, problems in the Euclidean plane, general convex bodies, computational complexity of lattice point problem, centrally symmetric convex bodies, reduction theory, and lattices and the space of lattices. The text then examines finite packing and covering and tilings, including plane tilings, monohedral tilings, bin packing, and sausage problems. The manuscript takes a look at valuations and dissections, geometric crystallography, convexity and differential geometry, and convex functions. Topics include differentiability, inequalities, uniqueness theorems for convex hypersurfaces, mixed discriminants and mixed volumes, differential geometric characterization of convexity, reduction of quadratic forms, and finite groups of symmetry operations. The selection is a dependable source of data for mathematicians and researchers interested in convex geometry.

Measures of Symmetry for Convex Sets and Stability

Author : Gabor Toth
Publisher : Springer
ISBN 13 : 3319237330
Total Pages : 278 pages
Book Rating : 4.3/5 (192 download)

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Book Synopsis Measures of Symmetry for Convex Sets and Stability by : Gabor Toth

Download or read book Measures of Symmetry for Convex Sets and Stability written by Gabor Toth and published by Springer. This book was released on 2015-11-26 with total page 278 pages. Available in PDF, EPUB and Kindle. Book excerpt: This textbook treats two important and related matters in convex geometry: the quantification of symmetry of a convex set—measures of symmetry—and the degree to which convex sets that nearly minimize such measures of symmetry are themselves nearly symmetric—the phenomenon of stability. By gathering the subject’s core ideas and highlights around Grünbaum’s general notion of measure of symmetry, it paints a coherent picture of the subject, and guides the reader from the basics to the state-of-the-art. The exposition takes various paths to results in order to develop the reader’s grasp of the unity of ideas, while interspersed remarks enrich the material with a behind-the-scenes view of corollaries and logical connections, alternative proofs, and allied results from the literature. Numerous illustrations elucidate definitions and key constructions, and over 70 exercises—with hints and references for the more difficult ones—test and sharpen the reader’s comprehension. The presentation includes: a basic course covering foundational notions in convex geometry, the three pillars of the combinatorial theory (the theorems of Carathéodory, Radon, and Helly), critical sets and Minkowski measure, the Minkowski–Radon inequality, and, to illustrate the general theory, a study of convex bodies of constant width; two proofs of F. John’s ellipsoid theorem; a treatment of the stability of Minkowski measure, the Banach–Mazur metric, and Groemer’s stability estimate for the Brunn–Minkowski inequality; important specializations of Grünbaum’s abstract measure of symmetry, such as Winternitz measure, the Rogers–Shepard volume ratio, and Guo’s Lp -Minkowski measure; a construction by the author of a new sequence of measures of symmetry, the kth mean Minkowski measure; and lastly, an intriguing application to the moduli space of certain distinguished maps from a Riemannian homogeneous space to spheres—illustrating the broad mathematical relevance of the book’s subject.

Handbook of Discrete and Computational Geometry

Author : Csaba D. Toth
Publisher : CRC Press
ISBN 13 : 1498711421
Total Pages : 1928 pages
Book Rating : 4.4/5 (987 download)

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Book Synopsis Handbook of Discrete and Computational Geometry by : Csaba D. Toth

Download or read book Handbook of Discrete and Computational Geometry written by Csaba D. Toth and published by CRC Press. This book was released on 2017-11-22 with total page 1928 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Handbook of Discrete and Computational Geometry is intended as a reference book fully accessible to nonspecialists as well as specialists, covering all major aspects of both fields. The book offers the most important results and methods in discrete and computational geometry to those who use them in their work, both in the academic world—as researchers in mathematics and computer science—and in the professional world—as practitioners in fields as diverse as operations research, molecular biology, and robotics. Discrete geometry has contributed significantly to the growth of discrete mathematics in recent years. This has been fueled partly by the advent of powerful computers and by the recent explosion of activity in the relatively young field of computational geometry. This synthesis between discrete and computational geometry lies at the heart of this Handbook. A growing list of application fields includes combinatorial optimization, computer-aided design, computer graphics, crystallography, data analysis, error-correcting codes, geographic information systems, motion planning, operations research, pattern recognition, robotics, solid modeling, and tomography.

Selected Topics in Convex Geometry

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

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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

Handbook of the Geometry of Banach Spaces

Author :
Publisher : Elsevier
ISBN 13 : 9780080533506
Total Pages : 870 pages
Book Rating : 4.5/5 (335 download)

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Book Synopsis Handbook of the Geometry of Banach Spaces by :

Download or read book Handbook of the Geometry of Banach Spaces written by and published by Elsevier. This book was released on 2003-05-06 with total page 870 pages. Available in PDF, EPUB and Kindle. Book excerpt: Handbook of the Geometry of Banach Spaces

Convex Geometric Analysis

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

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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.

Lectures On Convex Sets (Second Edition)

Author : Valeriu Soltan
Publisher : World Scientific
ISBN 13 : 9811202133
Total Pages : 611 pages
Book Rating : 4.8/5 (112 download)

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Book Synopsis Lectures On Convex Sets (Second Edition) by : Valeriu Soltan

Download or read book Lectures On Convex Sets (Second Edition) written by Valeriu Soltan and published by World Scientific. This book was released on 2019-11-28 with total page 611 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book provides a self-contained and systematic treatment of algebraic and topological properties of convex sets in the n-dimensional Euclidean space. It benefits advanced undergraduate and graduate students with various majors in mathematics, optimization, and operations research. It may be adapted as a primary book or an additional text for any course in convex geometry or convex analysis, aimed at non-geometers. It can be a source for independent study and a reference book for researchers in academia.The second edition essentially extends and revises the original book. Every chapter is rewritten, with many new theorems, examples, problems, and bibliographical references included. It contains three new chapters and 100 additional problems with solutions.