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The Resource Measures of symmetry for convex sets and stability, Gabor Toth

Measures of symmetry for convex sets and stability, Gabor Toth

Label
Measures of symmetry for convex sets and stability
Title
Measures of symmetry for convex sets and stability
Statement of responsibility
Gabor Toth
Creator
Author
Subject
Genre
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 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
Member of
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
Instantiates
Publication
Note
Textbook
Bibliography note
Includes bibliographical references (pages 267-273) 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
Publication
Note
Textbook
Bibliography note
Includes bibliographical references (pages 267-273) 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

Library Locations

    • Mathematical Sciences LibraryBorrow it
      104 Ellis Library, Columbia, MO, 65201, US
      38.944377 -92.326537
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