TY  - BOOK
AU  - Alonso-Gutierrez,David
AU  - Bastero,Jesus
TI  - Approaching the Kannan-Lovasz-Simonovits and variance conjectures
T2  - Lecture notes in mathematics ; 
SN  - 9783319132624
U1  - 515.1 23
PY  - 2015///
CY  - Switzerland
PB  - Springer
KW  - Geometric analysis.
KW  - Functional analysis
N1  - Includes index; 1. The Conjectures --
2. Main Examples --
3. Relating the Conjectures --
A.  Appendix --
Index
N2  - This Lecture Notes present the theory in an accessible way, so that interested readers, even those who are not experts in the field, will be able to appreciate the topics treated. Employing a style suitable for professionals with little background in analysis, geometry or probability, the work goes directly to the connection between isoperimetric-type inequalities and functional inequalities, allowing readers to quickly access the core of these conjectures. In addition, four recent and important results concerning this theory are presented. The first two are theorems attributed to Eldan-Klartag and Ball-Nguyen, which relate the variance and the KLS conjectures, respectively, to the hyperplane conjecture. The remaining two present in detail the main ideas needed to prove the best known estimate for the thin-shell width given by Guédon-Milman, and an approach to Eldan?s work on the connection between the thin-shell width and the KLS conjecture.
ER  -