{"product_id":"measures-of-symmetry-for-convex-sets-and-stability-9783319237329","title":"Measures of Symmetry for Convex Sets and Stability","description":"\u003cp\u003e • Author(s): Gabor Toth\u003cbr\u003e • Publisher: Springer Verlag\u003cbr\u003e • Publisher Imprint: Springer\u003cbr\u003e • Subject: Mathematics and Statistics\u003cbr\u003e • BISAC: Geometry - Analytic\u003c\/p\u003e\u003cp\u003e\u003c\/p\u003e\u003cp\u003e\u003cb\u003eFrom the Back Cover\u003c\/b\u003e\u003cbr\u003e\u003c\/p\u003e\u003cp\u003eThis 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.\u003c\/p\u003e\u003cp\u003eThe 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 \u003ci\u003eL\u003csup\u003ep\u003c\/sup\u003e\u003c\/i\u003e -Minkowski measure; a construction by the author of a new sequence of measures of symmetry, the \u003ci\u003ek\u003c\/i\u003eth mean Minkowski measure; and lastly, an intriguing application to the moduli space of certain distinguished maps from a Riemannian homogeneous space to\u003c\/p\u003e spheres--illustrating the broad mathematical relevance of the book's subject.\u003cp\u003e\u003c\/p\u003e","brand":"Springer Verlag","offers":[{"title":"Paperback","offer_id":45091593945239,"sku":"9783319237329","price":4675.0,"currency_code":"INR","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0666\/3471\/1191\/files\/9783319237329.webp?v=1769204720","url":"https:\/\/atlanticbooks.com\/products\/measures-of-symmetry-for-convex-sets-and-stability-9783319237329","provider":"Atlantic Books","version":"1.0","type":"link"}