Some Connections Between Isoperimetric And Sobolev Type Inequalities
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Some Connections between Isoperimetric and Sobolev-type Inequalities
Author: Serguei Germanovich Bobkov
language: en
Publisher: American Mathematical Soc.
Release Date: 1997
For Borel probability measures on metric spaces, this text studies the interplay between isoperimetric and Sobolev-type inequalities. In particular the question of finding optimal constants via isoperimetric quantities is explored. Also given are necessary and sufficient conditions for the equivalence between the extremality of some sets in the isoperimetric problem and the validity of some analytic inequalities. The book devotes much attention to: the probability distributions on the real line; the normalized Lebesgue measure on the Euclidean sheres; and the canonical Gaussian measure on the Euclidean space.
Concentration, Functional Inequalities and Isoperimetry
Author: Christian Houdré
language: en
Publisher: American Mathematical Soc.
Release Date: 2011
The interactions between concentration, isoperimetry and functional inequalities have led to many significant advances in functional analysis and probability theory. Important progress has also taken place in combinatorics, geometry, harmonic analysis and mathematical physics, with recent new applications in random matrices and information theory. This will appeal to graduate students and researchers interested in the interplay between analysis, probability, and geometry.
Relations Related to Betweenness: Their Structure and Automorphisms
Author: Samson Adepoju Adeleke
language: en
Publisher: American Mathematical Soc.
Release Date: 1998
This volume is about tree-like structures, namely semilinear ordering, general betweenness relations, C-relations and D-relations. It contains a systematic study of betweenness and introduces C- and D- relations to describe the behaviour of points at infinity (leaves or ends or directions of trees). The focus is on structure theorems and on automorphism groups, with applications to the theory of infinite permutation groups.