| 书目名称 | Measures of Symmetry for Convex Sets and Stability | | 编辑 | Gabor Toth | | 视频video | | | 概述 | Starting from the basics, provides a coherent and up-to-date account of various quantitative measures of symmetry arising in convex geometry.Contains over 90 challenging problems, with hints and refer | | 丛书名称 | Universitext | | 图书封面 |  | | 描述 | .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 mea | | 出版日期 | Textbook 2015 | | 关键词 | Banach-Mazur metric; Groemer stability of the Brunn-Minkowsi inequality; Gruenbaum‘s general notion of | | 版次 | 1 | | doi | https://doi.org/10.1007/978-3-319-23733-6 | | isbn_softcover | 978-3-319-23732-9 | | isbn_ebook | 978-3-319-23733-6Series ISSN 0172-5939 Series E-ISSN 2191-6675 | | issn_series | 0172-5939 | | copyright | Springer International Publishing Switzerland 2015 |
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发表于 2025-3-21 17:57:33
