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# ðŸ“™ Geometry of isotropic convex bodies by Silouanos Brazitikos, Apostolos Giannopoulos, Petros Valettas, Beatrice-helen Vritsiou â€” download pdf

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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 normalization, 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-LovÃ¡sz-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

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- Series:
**Mathematical Surveys and Monographs 196** - Author:
**Silouanos Brazitikos, Apostolos Giannopoulos, Petros Valettas, Beatrice-helen Vritsiou** - Year:
**2014** - Publisher:
**American Mathematical Society** - Language:
**English** - ISBN:
**1470414562,978-1-4704-1456-6**

- File size:
**3 927 339** - Format:
**pdf**

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The study of the geometry of convex bodies based on information about sections and projections of these bodies has important applications in many areas of mathematics and science. In this book, a new Fourier analysis approach is discussed. The idea is to ...

The study of the geometry of convex bodies based on information about sections and projections of these bodies has important applications in many areas of mathematics and science. In this book, a new Fourier analysis approach is discussed. The idea is to ...

Convex bodies are at once simple and amazingly rich in structure. While the classical results go back many decades, during the past ten years the integral geometry of convex bodies has undergone a dramatic revitalization, brought about by the introductio...

This work deals with scattering by obstacles which are finite disjoint unions of strictly convex bodies with smooth boundaries in an odd dimensional Euclidean space. The class of obstacles of this type is considered which are contained in a given (large) ...

This collection of original papers related to the Israeli GAFA seminar (on Geometric Aspects of Functional Analysis) during the years 2004-2005 follows the long tradition of the previous volumes that reflect the general trends of the Theory and are a sour...

The field of convex geometry has become a fertile subject of mathematical activity in the past few decades. This exposition, examining in detail those topics in convex geometry that are concerned with Euclidean space, is enriched by numerous examples, ill...

Optimization is the science of making a best choice in the face of conflicting requirements. Any convex optimization problem has geometric interpretation. If a given optimization problem can be transformed to a convex equivalent, then this interpretive ...

This textbook treats two important and related matters in convex geometry: the quantification of symmetry of a convex setâ€•measures of symmetryâ€•and the degree to which convex sets that nearly minimize such measures of symmetry are themselves nearly symmetr...

Information geometry, which began as an investigation of the natural differential geometric structure possessed by families of probability distributions, is offered here in a complete treatment, translated from the original 1993 work in Japanese. The topi...

Rendering complex material accessible to the novice and expert alike, this unique resource details laboratory and industrial synthesis and applications of oligomers;suggesting practical solutions to on-the-job problems as well as exploring processing devi...

A staple food for thousands of years in the Mediterranean region, olive oil is now becoming popular all over the world. Olive oil has several unique characteristics that set it apart from other vegetable oils. Recent research suggests that olive oil produ...

Optical Polarization in Biomedical Applications introduces key developments in optical polarization methods for quantitative studies of tissues, while presenting the theory of polarization transfer in a random medium as a basis for the quantitative descr...

A revision of the senior/graduate level text for courses dealing with the theory and application of Optical Fiber Communication Technology, this book progresses from descriptions of the individual elements of an optical communications system to an analysi...

Written by a pioneer in the field, this unique volume is the only one of its kind to explore advanced concepts in the mathematical representation of polarization, descriptors, and various optical elements used in the analysis of polarization in multiple a...

A singular resource covering cutting-edge information and research in the exploding field of optomechanical engineering! Optomechanical Engineering Handbook on CD-ROM...