Cargando…
Measures of Symmetry for Convex Sets and Stability
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...
| Clasificación: | Libro Electrónico |
|---|---|
| Autor principal: | |
| Autor Corporativo: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Cham :
Springer International Publishing : Imprint: Springer,
2015.
|
| Edición: | 1st ed. 2015. |
| Colección: | Universitext,
|
| Temas: | |
| Acceso en línea: | Texto Completo |
MARC
| LEADER | 00000nam a22000005i 4500 | ||
|---|---|---|---|
| 001 | 978-3-319-23733-6 | ||
| 003 | DE-He213 | ||
| 005 | 20220117085838.0 | ||
| 007 | cr nn 008mamaa | ||
| 008 | 151126s2015 sz | s |||| 0|eng d | ||
| 020 | |a 9783319237336 |9 978-3-319-23733-6 | ||
| 024 | 7 | |a 10.1007/978-3-319-23733-6 |2 doi | |
| 050 | 4 | |a QA639.5-640.7 | |
| 050 | 4 | |a QA640.7-640.77 | |
| 072 | 7 | |a PBM |2 bicssc | |
| 072 | 7 | |a PBD |2 bicssc | |
| 072 | 7 | |a MAT012020 |2 bisacsh | |
| 072 | 7 | |a PBM |2 thema | |
| 072 | 7 | |a PBD |2 thema | |
| 082 | 0 | 4 | |a 516 |2 23 |
| 100 | 1 | |a Toth, Gabor. |e author. |4 aut |4 http://id.loc.gov/vocabulary/relators/aut | |
| 245 | 1 | 0 | |a Measures of Symmetry for Convex Sets and Stability |h [electronic resource] / |c by Gabor Toth. |
| 250 | |a 1st ed. 2015. | ||
| 264 | 1 | |a Cham : |b Springer International Publishing : |b Imprint: Springer, |c 2015. | |
| 300 | |a XII, 278 p. 65 illus., 1 illus. in color. |b online resource. | ||
| 336 | |a text |b txt |2 rdacontent | ||
| 337 | |a computer |b c |2 rdamedia | ||
| 338 | |a online resource |b cr |2 rdacarrier | ||
| 347 | |a text file |b PDF |2 rda | ||
| 490 | 1 | |a Universitext, |x 2191-6675 | |
| 505 | 0 | |a First Things First on Convex Sets -- Affine Diameters and the Critical Set -- Measures of Stability and Symmetry -- Mean Minkowski Measures. | |
| 520 | |a 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. | ||
| 650 | 0 | |a Convex geometry . | |
| 650 | 0 | |a Discrete geometry. | |
| 650 | 1 | 4 | |a Convex and Discrete Geometry. |
| 710 | 2 | |a SpringerLink (Online service) | |
| 773 | 0 | |t Springer Nature eBook | |
| 776 | 0 | 8 | |i Printed edition: |z 9783319237329 |
| 776 | 0 | 8 | |i Printed edition: |z 9783319237343 |
| 830 | 0 | |a Universitext, |x 2191-6675 | |
| 856 | 4 | 0 | |u https://doi.uam.elogim.com/10.1007/978-3-319-23733-6 |z Texto Completo |
| 912 | |a ZDB-2-SMA | ||
| 912 | |a ZDB-2-SXMS | ||
| 950 | |a Mathematics and Statistics (SpringerNature-11649) | ||
| 950 | |a Mathematics and Statistics (R0) (SpringerNature-43713) | ||