# Some Connections between Isoperimetric and Sobolev-type Inequalities

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*Serguei G. Bobkov; Christian Houdré*

#### Table of Contents

# Table of Contents

## Some Connections between Isoperimetric and Sobolev-type Inequalities

- Table of Contents vii8 free
- Abstract viii9 free
- 1 Introduction 110 free
- 2 Differential and integral forms of isoperimetric inequalities 1928 free
- 3 Proof of Theorem 1.1 2534
- 4 A relation between the distribution of a function and its derivative 3140
- 5 A variational problem 3443
- 6 The discrete version of Theorem 5.1 4554
- 7 Proof of Propositions 1.3 and 1.5 5968
- 8 A special case of Theorem 1.2 6372
- 9 The uniform distribution on the sphere 6675
- 10 Existence of optimal Orlicz spaces 7079
- 11 Proof of Theorem 1.9 (the case of the sphere) 7786
- 12 Proof of Theorem 1.9 (the Gaussian case) 8594
- 13 The isoperimetric problem on the real line 8796
- 14 Isoperimetric and Sobolev-type inequalities on the real line 98107
- 15 Extensions of Sobolev-type inequalities to product measures on R[sup(n)] 106115
- References 109118