Measures of Symmetry for Convex Sets and Stability is popular PDF and ePub book, written by Gabor Toth in 2015, it is a fantastic choice for those who relish reading online the Uncategoriezed genre. Let's immerse ourselves in this engaging Uncategoriezed book by exploring the summary and details provided below. Remember, Measures of Symmetry for Convex Sets and Stability can be Read Online from any device for your convenience.
Measures of Symmetry for Convex Sets and Stability Book PDF 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.
Detail Book of Measures of Symmetry for Convex Sets and Stability PDF
- Author : Gabor Toth
- Release : 03 July 2024
- Publisher : Unknown
- ISBN : 3319237349
- Genre : Uncategoriezed
- Total Page : null pages
- Language : English
- PDF File Size : 7,9 Mb
If you're still pondering over how to secure a PDF or EPUB version of the book Measures of Symmetry for Convex Sets and Stability by Gabor Toth, don't worry! All you have to do is click the 'Get Book' buttons below to kick off your Download or Read Online journey. Just a friendly reminder: we don't upload or host the files ourselves.