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Author : E. Asplund
Publisher :
ISBN 13 :
Total Pages : 14 pages
Book Rating : 4.3/5 (91 download)
Download or read book On a Measure of Asymmetry of Convex Bodies written by E. Asplund and published by . This book was released on 1960 with total page 14 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Gabor Toth
Publisher : Springer
ISBN 13 : 3319237330
Total Pages : 278 pages
Book Rating : 4.3/5 (192 download)
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.
Author : E. Asplund
Publisher :
ISBN 13 :
Total Pages : 8 pages
Book Rating : 4.3/5 (91 download)
Download or read book A Measure of Asymmetry for Convex Surfaces written by E. Asplund and published by . This book was released on 1960 with total page 8 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Rolf Schneider
Publisher : Cambridge University Press
ISBN 13 : 1107601010
Total Pages : 759 pages
Book Rating : 4.1/5 (76 download)
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.
Author : Horst Martini
Publisher : Springer
ISBN 13 : 3030038688
Total Pages : 486 pages
Book Rating : 4.0/5 (3 download)
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.
Author :
Publisher :
ISBN 13 :
Total Pages : 224 pages
Book Rating : 4.:/5 (31 download)
Download or read book U.S. Government Research Reports written by and published by . This book was released on 1963 with total page 224 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Rolf Schneider
Publisher : Cambridge University Press
ISBN 13 : 0521352207
Total Pages : 506 pages
Book Rating : 4.5/5 (213 download)
Download or read book Convex Bodies written by Rolf Schneider and published by Cambridge University Press. This book was released on 1993-02-25 with total page 506 pages. Available in PDF, EPUB and Kindle. Book excerpt: A comprehensive introduction to convex bodies giving full proofs for some deeper theorems which have never previously been brought together.
Author : Victor Klee
Publisher : American Mathematical Soc.
ISBN 13 : 0821814079
Total Pages : 516 pages
Book Rating : 4.8/5 (218 download)
Download or read book Convexity written by Victor Klee and published by American Mathematical Soc.. This book was released on 1963 with total page 516 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Gabor Toth
Publisher :
ISBN 13 : 9783319237343
Total Pages : pages
Book Rating : 4.2/5 (373 download)
Download or read book Measures of Symmetry for Convex Sets and Stability written by Gabor Toth and published by . This book was released on 2015 with total page 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.
Author : Silouanos Brazitikos
Publisher : American Mathematical Soc.
ISBN 13 : 1470414562
Total Pages : 618 pages
Book Rating : 4.4/5 (74 download)
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 618 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.
Author : Hallard T. Croft
Publisher : Springer Science & Business Media
ISBN 13 : 1461209633
Total Pages : 213 pages
Book Rating : 4.4/5 (612 download)
Download or read book Unsolved Problems in Geometry written by Hallard T. Croft and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 213 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematicians and non-mathematicians alike have long been fascinated by geometrical problems, particularly those that are intuitive in the sense of being easy to state, perhaps with the aid of a simple diagram. Each section in the book describes a problem or a group of related problems. Usually the problems are capable of generalization of variation in many directions. The book can be appreciated at many levels and is intended for everyone from amateurs to research mathematicians.
Author : H. Groemer
Publisher : Cambridge University Press
ISBN 13 : 0521473187
Total Pages : 343 pages
Book Rating : 4.5/5 (214 download)
Download or read book Geometric Applications of Fourier Series and Spherical Harmonics written by H. Groemer and published by Cambridge University Press. This book was released on 1996-09-13 with total page 343 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a comprehensive presentation of geometric results, primarily from the theory of convex sets, that have been proved by the use of Fourier series or spherical harmonics. An important feature of the book is that all necessary tools from the classical theory of spherical harmonics are presented with full proofs. These tools are used to prove geometric inequalities, stability results, uniqueness results for projections and intersections by hyperplanes or half-spaces and characterisations of rotors in convex polytopes. Again, full proofs are given. To make the treatment as self-contained as possible the book begins with background material in analysis and the geometry of convex sets. This treatise will be welcomed both as an introduction to the subject and as a reference book for pure and applied mathematics.
Author : Steven R. Finch
Publisher : Cambridge University Press
ISBN 13 : 9780521818056
Total Pages : 634 pages
Book Rating : 4.8/5 (18 download)
Download or read book Mathematical Constants written by Steven R. Finch and published by Cambridge University Press. This book was released on 2003-08-18 with total page 634 pages. Available in PDF, EPUB and Kindle. Book excerpt: Steven Finch provides 136 essays, each devoted to a mathematical constant or a class of constants, from the well known to the highly exotic. This book is helpful both to readers seeking information about a specific constant, and to readers who desire a panoramic view of all constants coming from a particular field, for example, combinatorial enumeration or geometric optimization. Unsolved problems appear virtually everywhere as well. This work represents an outstanding scholarly attempt to bring together all significant mathematical constants in one place.
Author : Emil Grosswald
Publisher : American Mathematical Soc.
ISBN 13 : 0821851551
Total Pages : 612 pages
Book Rating : 4.8/5 (218 download)
Download or read book A Tribute to Emil Grosswald written by Emil Grosswald and published by American Mathematical Soc.. This book was released on 1993 with total page 612 pages. Available in PDF, EPUB and Kindle. Book excerpt: Emil Grosswald was a mathematician of great accomplishment and remarkable breadth of vision. This volume pays tribute to the span of his mathematical interests, which is reflected in the wide range of papers collected here. With contributions by leading contemporary researchers in number theory, modular functions, combinatorics, and related analysis, this book will interest graduate students and specialists in these fields. The high quality of the articles and their close connection to current research trends make this volume a must for any mathematics library.
Author : Gerard Meurant
Publisher : Elsevier
ISBN 13 : 0080934390
Total Pages : 801 pages
Book Rating : 4.0/5 (89 download)
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.
Author : Tommy Bonnesen
Publisher :
ISBN 13 :
Total Pages : 192 pages
Book Rating : 4.3/5 (91 download)
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:
Author :
Publisher :
ISBN 13 :
Total Pages : 940 pages
Book Rating : 4.3/5 (91 download)
Download or read book Mathematical Reviews written by and published by . This book was released on 2006 with total page 940 pages. Available in PDF, EPUB and Kindle. Book excerpt:
