ENGLISH

Asymptotic Theory of Finite Dimensional Normed Spaces: Isoperimetric Inequalities in Riemannian Manifolds

By Vitali D. Milman , Gideon Schechtman

Book information

Publisher
Springer
Year
2002
ISBN
3540167692, 9783540167693
LCC
QA3 .L28 no. 1200,QA322.2 .L28 no. 1200
Language
english
Format
PDF
Filesize
6 MB (6338818 bytes)
Series
Lecture Notes in Mathematics
Pages
166\165
Time added
2011-06-04 13:46:07

Description

Vol. 1200 of the LNM series deals with the geometrical structure of finite dimensional normed spaces. One of the main topics is the estimation of the dimensions of euclidean and l^n p spaces which nicely embed into diverse finite-dimensional normed spaces. An essential method here is the concentration of measure phenomenon which is closely related to large deviation inequalities in Probability on the one hand, and to isoperimetric inequalities in Geometry on the other. The book contains also an appendix, written by M. Gromov, which is an introduction to isoperimetric inequalities on riemannian manifolds. Only basic knowledge of Functional Analysis and Probability is expected of the reader. The book can be used (and was used by the authors) as a text for a first or second graduate course. The methods used here have been useful also in areas other than Functional Analysis (notably, Combinatorics).

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