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The \(AB\) Program in Geometric Analysis: Sharp Sobolev Inequalities and Related Problems
Olivier Druet and Emmanuel Hebey, University of Cergy-Pontoise, France

Memoirs of the American Mathematical Society
2002; 98 pp; softcover
Volume: 160
ISBN-10: 0-8218-2989-0
ISBN-13: 978-0-8218-2989-9
List Price: US$59
Individual Members: US$35.40
Institutional Members: US$47.20
Order Code: MEMO/160/761
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Function theory and Sobolev inequalities have been the target of investigatio for decades. Sharp constants in these inequalities constitute a critical tool in geometric analysis. The \(AB\) program is concerned with sharp Sobolev inequalities on compact Riemannian manifolds. Important and significant progress has been made during recent years. We summarize the present state ad describe new results.


Graduate students and research mathematicians interested in global analysis and analysis on manifolds.

Table of Contents

  • Euclidean background
  • Statement of the \(AB\) program
  • Some historical motivations
  • The \(H^2_1\)-inequality--Part I
  • The \(H^2_1\)-inequality--Part II
  • PDE methods
  • The isoperimetric inequality
  • The \(H^p_1\)-inequalities, \(1 < p < \mathrm{dim}M\)
  • Bibliography
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