# Some connections between isoperimetric and Sobolev-type inequalities

### About this Title

**Serguei G. Bobkov** and **Christian Houdré**

Publication: Memoirs of the American Mathematical Society

Publication Year
1997: Volume 129, Number 616

ISBNs: 978-0-8218-0642-5 (print); 978-1-4704-0201-3 (online)

DOI: http://dx.doi.org/10.1090/memo/0616

MathSciNet review: 1396954

MSC: Primary 46E35; Secondary 49Q20, 60E15

### Table of Contents

**Chapters**

- 1. Introduction
- 2. Differential and integral forms of isoperimetric inequalities
- 3. Proof of Theorem 1.1
- 4. A relation between the distribution of a function and its derivative
- 5. A variational problem
- 6. The discrete version of Theorem 5.1
- 7. Proof of Propositions 1.3 and 1.5
- 8. A special case of Theorem 1.2
- 9. The uniform distribution on the sphere
- 10. Existence of optimal Orlicz spaces
- 11. Proof of Theorem 1.9 (the case of the sphere)
- 12. Proof of Theorem 1.9 (the Gaussian case)
- 13. The isoperimetric problem on the real line
- 14. Isoperimetric and Sobolev-type inequalities on the real line
- 15. Extensions of Sobolev-type inequalities to product measures on $\mathbf {R}^n$