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Item Details
| Title:
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MEASURES OF SYMMETRY FOR CONVEX SETS AND STABILITY
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| By: |
Gabor Toth |
| Format: |
Paperback |
| List price:
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£54.99 |
| Our price: |
£46.74 |
| Discount: |
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| You save:
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£8.25 |
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| ISBN 10: |
3319237322 |
| ISBN 13: |
9783319237329 |
| Availability: |
Usually dispatched within 1-3 weeks.
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| Stock: |
Currently 0 available |
| Publisher: |
SPRINGER INTERNATIONAL PUBLISHING AG |
| Pub. date: |
27 November, 2015 |
| Edition: |
1st ed. 2015 |
| Series: |
Universitext |
| Pages: |
278 |
| Description: |
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. |
| Synopsis: |
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 Grunbaum'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 Caratheodory, 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 Grunbaum'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. |
| Illustrations: |
1 Illustrations, color; 64 Illustrations, black and white; XII, 278 p. 65 |
| Publication: |
Switzerland |
| Imprint: |
Springer International Publishing AG |
| Returns: |
Returnable |
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