AMS eBook CollectionsOne of the world's most respected mathematical collections, available in digital format for your library or institution

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/10.1090/surv/196
MathSciNet review: MR3185453
MSC: Primary 52-02; Secondary 28Axx, 46Bxx, 52Axx, 60D05

View full volume as PDF

Read more about this volume

Table of Contents

Download chapters as PDF

Front/Back Matter

• View this volume's front and 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