1 Table of Contents: “.... Reilly's formula and applications; 9. Isoperimetric inequalities and Sobolev inequalities; 10. The heat...”

2 Table of Contents: “... and Talagrand's inequality -- Log-Sobolev inequalities and concentration -- Appendix A : summary of the most...”

3 Table of Contents: “... -- Isoperimetric and Sobolev inequalities in sharp form -- Displacement convexity and equilibrium of gases...”

4 “... and information. These include the logarithmic Sobolev inequality, which measures how fast some physical systems...”

5 Table of Contents: “... --Logarithmic Sobolev inequality for diffusion semigroups / Ivan Gentil -- Lecture notes on variational models...”

6 “... and Sobolev inequalities. The text provides the first self contained account of the equivalence between...”

7 “..., hypercontractive and logarithmic Sobolev inequalities, Beckner's inequality, and many, many more. The inequalities...”