Geometry of Isotropic Convex Bodies
About this Title
Silouanos Brazitikos, University of Athens, Athens, Greece, Apostolos Giannopoulos, University of Athens, Athens, Greece, Petros Valettas, Texas A & M University, College Station, TX and Beatrice-Helen Vritsiou, University of Athens, Athens, Greece
Publication: Mathematical Surveys and Monographs
Publication Year:
2014; Volume 196
ISBNs: 978-1-4704-1456-6 (print); 978-1-4704-1526-6 (online)
DOI: https://doi.org/http://dx.doi.org/10.1090/surv/196
MathSciNet review: MR3185453
MSC: Primary 52-02; Secondary 28Axx, 46Bxx, 52Axx, 60D05
Table of Contents
Front/Back Matter
Chapters
- Chapter 1. Background from asymptotic convex geometry
- Chapter 2. Isotropic log-concave measures
- Chapter 3. Hyperplane conjecture and Bourgain’s upper bound
- Chapter 4. Partial answers
- Chapter 5. $L_q$-centroid bodies and concentration of mass
- Chapter 6. Bodies with maximal isotropic constant
- Chapter 7. Logarithmic Laplace transform and the isomorphic slicing problem
- Chapter 8. Tail estimates for linear functionals
- Chapter 9. $M$ and $M*$-estimates
- Chapter 10. Approximating the covariance matrix
- Chapter 11. Random polytopes in isotropic convex bodies
- Chapter 12. Central limit problem and the thin shell conjecture
- Chapter 13. The thin shell estimate
- Chapter 14. Kannan-Lovász-Simonovits conjecture
- Chapter 15. Infimum convolution inequalities and concentration
- Chapter 16. Information theory and the hyperplane conjecture