1. Introduction and notations 2. Poincaré-type inequalities 3. Entropy and Orlicz spaces 4. $\mathrm {LS}_q$ and Hardy-type inequalities on the line 5. Probability measures satisfying $\mathrm {LS}_q$-inequalities on the real line 6. Exponential integrability and perturbation of measures 7. $\mathrm {LS}_q$-inequalities for Gibbs measures with super Gaussian tails 8. $\mathrm {LS}_q$-inequalities and Markov semigroups 9. Isoperimetry 10. The localization argument 11. Infinitesimal version 12. Proof of Theorem 9.2 13. Euclidean distance (proof of Theorem 9.1) 14. Uniformly convex bodies 15. From isoperimetry to $\mathrm {LS}_q$-inequalities 16. Isoperimetric functional inequalities
Summary
Introduction and notations Poincare-type inequalities Entropy and Orlicz spaces $\mathbf{LS}_q$ and Hardy-type inequalities on the line Probability measures satisfying $\mathbf{LS}_q$-inequalities on the real line Exponential integrability and perturbation of measures $\mathbf{LS}_q$-inequalities for Gibbs measures with super Gaussian tails $\mathbf{LS}_q$-inequalities and Markov semigroups Isoperimetry The localization argument Infinitesimal version Proof of Theorem 9.2 Euclidean distance (proof of Theorem 9.1) Uniformly convex bodies From isoperimetry to $\mathbf{LS}_q$-inequalities Isoperimetric functional inequalities Bibliography
