The Resource Measures of symmetry for convex sets and stability, Gabor Toth
Measures of symmetry for convex sets and stability, Gabor Toth
Resource Information
The item Measures of symmetry for convex sets and stability, Gabor Toth represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in University of Missouri Libraries.This item is available to borrow from 1 library branch.
Resource Information
The item Measures of symmetry for convex sets and stability, Gabor Toth represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in University of Missouri Libraries.
This item is available to borrow from 1 library branch.
 Summary
 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 stateoftheart. 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 behindthescenes 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
 Language
 eng
 Extent
 xii, 278 pages
 Note
 Textbook
 Contents

 First Things First on Convex Sets
 Affine Diameters and the Critical Set
 Measures of Stability and Symmetry
 Mean Minkowski Measures
 Isbn
 9783319237329
 Label
 Measures of symmetry for convex sets and stability
 Title
 Measures of symmetry for convex sets and stability
 Statement of responsibility
 Gabor Toth
 Language
 eng
 Summary
 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 stateoftheart. 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 behindthescenes 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
 Cataloging source
 OHX
 http://library.link/vocab/creatorName
 Tóth, Gábor
 Illustrations
 illustrations
 Index
 index present
 LC call number
 QA639.5
 LC item number
 .T68 2015
 Literary form
 non fiction
 Nature of contents
 bibliography
 Series statement
 Universitext,
 http://library.link/vocab/subjectName

 Convex geometry
 Discrete geometry
 Convex geometry
 Discrete geometry
 Label
 Measures of symmetry for convex sets and stability, Gabor Toth
 Note
 Textbook
 Bibliography note
 Includes bibliographical references (pages 267273) and index
 Carrier category
 volume
 Carrier category code

 nc
 Carrier MARC source
 rdacarrier
 Content category
 text
 Content type code

 txt
 Content type MARC source
 rdacontent
 Contents
 First Things First on Convex Sets  Affine Diameters and the Critical Set  Measures of Stability and Symmetry  Mean Minkowski Measures
 Control code
 932125937
 Dimensions
 24 cm
 Extent
 xii, 278 pages
 Isbn
 9783319237329
 Lccn
 2015950621
 Media category
 unmediated
 Media MARC source
 rdamedia
 Media type code

 n
 Other control number
 9783319237329
 Other physical details
 illustrations
 System control number
 (OCoLC)932125937
 Label
 Measures of symmetry for convex sets and stability, Gabor Toth
 Note
 Textbook
 Bibliography note
 Includes bibliographical references (pages 267273) and index
 Carrier category
 volume
 Carrier category code

 nc
 Carrier MARC source
 rdacarrier
 Content category
 text
 Content type code

 txt
 Content type MARC source
 rdacontent
 Contents
 First Things First on Convex Sets  Affine Diameters and the Critical Set  Measures of Stability and Symmetry  Mean Minkowski Measures
 Control code
 932125937
 Dimensions
 24 cm
 Extent
 xii, 278 pages
 Isbn
 9783319237329
 Lccn
 2015950621
 Media category
 unmediated
 Media MARC source
 rdamedia
 Media type code

 n
 Other control number
 9783319237329
 Other physical details
 illustrations
 System control number
 (OCoLC)932125937
Subject
Genre
Member of
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