Geometry of Isotropic Convex Bodies
Silouanos Brazitikos · Apostolos Giannopoulos · Petros Valettas · Beatrice-Helen Vritsiou
апр. 2014 г. · Mathematical Surveys and Monographs Книга 196 · American Mathematical Soc.
Электронная книга
594
Количество страниц
reportОценки и отзывы не проверены. Подробнее…
Об электронной книге
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.
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-Lovász-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.
Оцените электронную книгу
Поделитесь с нами своим мнением.
Где читать книги
Смартфоны и планшеты
Установите приложение Google Play Книги для Android или iPad/iPhone. Оно синхронизируется с вашим аккаунтом автоматически, и вы сможете читать любимые книги онлайн и офлайн где угодно.
Ноутбуки и настольные компьютеры
Слушайте аудиокниги из Google Play в веб-браузере на компьютере.
Устройства для чтения книг
Чтобы открыть книгу на таком устройстве для чтения, как Kobo, скачайте файл и добавьте его на устройство. Подробные инструкции можно найти в Справочном центре.
