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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)
MathSciNet review: 1396954
MSC: Primary 46E35; Secondary 49Q20, 60E15

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Table of Contents


  • 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 $\mathbf {R}^n$