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The $AB$ program in geometric analysis: sharp Sobolev inequalities and related problems

About this Title

Olivier Druet and Emmanuel Hebey

Publication: Memoirs of the American Mathematical Society
Publication Year: 2002; Volume 160, Number 761
ISBNs: 978-0-8218-2989-9 (print); 978-1-4704-0359-1 (online)
DOI: https://doi.org/10.1090/memo/0761
MathSciNet review: 1938183
MSC: Primary 58J05; Secondary 35J20, 46E35, 53C21, 58E35

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Table of Contents

Chapters

  • 1. Euclidean background
  • 2. Statement of the $AB$ program
  • 3. Some historical motivations
  • 4. The $H^2_1$-inequality – Part I
  • 5. The $H^2_1$-inequality – Part II
  • 6. PDE methods
  • 7. The isoperimetric inequality
  • 8. The $H^p_1$-inequalities, $1 < p < \dim M$