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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 ...

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) ...

Focuses on the inverse problem of determining a rigid inclusion inside an isotropic elastic body [OMEGA], from a single measurement of traction and displacement taken on the boundary of [OMEGA]. For this severely ill - posed problem, the authors prove uni...

The theory and methodology of design of general-purpose machines that may be controlled by a computer to perform all the tasks of a set of special-purpose machines is the focus of modern machine design research. These seventeen contributions chronicle rec...

After having read this book you will never see birds in the same way again.The unexpected patterns displayed by a birdâ€™s body have been seen as bizarre events that demanded little attention or were described as â€˜amazing curiositiesâ€™.None of these surprisi...

This book presents the foundations of Euclidean geometry from the point of view of mathematics, taking advantage of all the developments since the appearance of Hilbert's classic work. Here, real affine space is characterized by a small number of axioms i...

The object of this book is to present the basic facts of convex functions, standard dynamical systems, descent numerical algorithms and some computer programs on Riemannian manifolds in a form suitable for applied mathematicians, scientists and engineers....

Subriemannian geometries, also known as Carnot-Caratheodory geometries, can be viewed as limits of Riemannian geometries. They also arise in physical phenomenon involving ""geometric phases"" or holonomy. Very roughly speaking, a subriemannian geometry co...

This is an collection of some easily-formulated problems that remain open in the study of the geometry and analysis of Banach spaces. Assuming the reader has a working familiarity with the basic results of Banach space theory, the authors focus on concept...

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...