**Memoirs of the American Mathematical Society**

2002;
98 pp;
Softcover

MSC: Primary 58;

Print ISBN: 978-0-8218-2989-9

Product Code: MEMO/160/761

List Price: $59.00

Individual Member Price: $35.40

**Electronic ISBN: 978-1-4704-0359-1
Product Code: MEMO/160/761.E**

List Price: $59.00

Individual Member Price: $35.40

# The \(AB\) Program in Geometric Analysis: Sharp Sobolev Inequalities and Related Problems

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*Olivier Druet; Emmanuel Hebey*

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.

#### Readership

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

#### Table of Contents

# Table of Contents

## The $AB$ Program in Geometric Analysis: Sharp Sobolev Inequalities and Related Problems

- Contents vii8 free
- Chapter 1. Euclidean background 110 free
- Chapter 2. Statement of the AB program 514
- Chapter 3. Some historical motivations 918
- Chapter 4. The H[sup(2)][sub(1)]–inequality – Part I 1322
- Chapter 5. The H[sup(2)][sub(1)]–inequality – Part II 2534
- 5.1. Sharp inequalities with respect to the A–constant 2534
- 5.2. Conformal sphere 2837
- 5.3. Subextremal functions and asymptotic studies 3140
- 5.4. Extremal functions for the A–part of the AB program 3342
- 5.5. Critical functions versus best constants 3948
- 5.6. Low dimension 4352
- 5.7. The B–part of the AB program 4655

- Chapter 6. PDE Methods 5160
- Chapter 7. The isoperimetric inequality 6574
- Chapter 8. The H[sup(p)][sub(1)]–inequalities, 1 < p < dimM 7584
- Bibliography 95104