Geometry of Isotropic Convex Bodies
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A01=Apostolos Giannopoulos
A01=Beatrice-Helen Vritsiou
A01=Petros Valettas
A01=Silouanos Brazitikos
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Author_Apostolos Giannopoulos
Author_Beatrice-Helen Vritsiou
Author_Petros Valettas
Author_Silouanos Brazitikos
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COP=United States
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Product details
- ISBN 9781470414566
- Weight: 1225g
- Dimensions: 178 x 254mm
- Publication Date: 30 May 2014
- Publisher: American Mathematical Society
- Publication City/Country: US
- Product Form: Hardback
- Language: English
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The study of high-dimensional convex bodies from a geometric and analytic point of view, with an emphasis on the dependence of various parameters on the dimension stands at the intersection of classical convex geometry and the local theory of Banach spaces. It is also closely linked to many other fields, such as probability theory, partial differential equations, Riemannian geometry, harmonic analysis and combinatorics. It is now understood that the convexity assumption forces most of the volume of a high-dimensional convex body to be concentrated in some canonical way and the main question is whether, under some natural normalisation, the answer to many fundamental questions should be independent of the dimension.
The aim of this book is to introduce a number of well-known questions regarding the distribution of volume in high-dimensional convex bodies, which are exactly of this nature: among them are the slicing problem, the thin-shell conjecture and the Kannan-Lovasz-Simonovits conjecture. This book provides a self-contained and up to date account of the progress that has been made in the last fifteen years.
The aim of this book is to introduce a number of well-known questions regarding the distribution of volume in high-dimensional convex bodies, which are exactly of this nature: among them are the slicing problem, the thin-shell conjecture and the Kannan-Lovasz-Simonovits conjecture. This book provides a self-contained and up to date account of the progress that has been made in the last fifteen years.
Silouanos Brazitikos, University of Athens, Greece.
Apostolos Giannopoulos, University of Athens, Greece.
Petros Valettas, Texas A & M University, College Station, TX.
Beatrice-Helen Vritsiou, University of Athens, Greece.
Apostolos Giannopoulos, University of Athens, Greece.
Petros Valettas, Texas A & M University, College Station, TX.
Beatrice-Helen Vritsiou, University of Athens, Greece.
