The Hypoelliptic Laplacian and Ray-Singer Metrics. (AM-167) / / Gilles Lebeau, Jean-Michel Bismut.

• Superior document: Title is part of eBook package: De Gruyter Princeton Annals of Mathematics eBook-Package 1940-2020
• VerfasserIn: Bismut, Jean-Michel,; Lebeau, Gilles,
• Place / Publishing House: Princeton, NJ : : Princeton University Press, , [2008]; ©2009
• Year of Publication: 2008
• Edition: Course Book
• Language: English
• Series: Annals of Mathematics Studies ; 167
• Physical Description: 1 online resource (376 p.) :; 4 line illus.

This book presents the analytic foundations to the theory of the hypoelliptic Laplacian. The hypoelliptic Laplacian, a second-order operator acting on the cotangent bundle of a compact manifold, is supposed to interpolate between the classical Laplacian and the geodesic flow. Jean-Michel Bismut and...

Table of Contents

• Frontmatter
• Contents
• Introduction
• Chapter 1. Elliptic Riemann-Roch-Grothendieck and flat vector bundles
• Chapter 2. The hypoelliptic Laplacian on the cotangent bundle
• Chapter 3. Hodge theory, the hypoelliptic Laplacian and its heat kernel
• Chapter 4. Hypoelliptic Laplacians and odd Chern forms
• Chapter 5. The limit as t → +∞ and b → 0 of the superconnection forms
• Chapter 6. Hypoelliptic torsion and the hypoelliptic Ray-Singer metrics
• Chapter 7. The hypoelliptic torsion forms of a vector bundle
• Chapter 8. Hypoelliptic and elliptic torsions: a comparison formula
• Chapter 9. A comparison formula for the Ray-Singer metrics
• Chapter 10. The harmonic forms for b → 0 and the formal Hodge theorem
• Chapter 11. A proof of equation (8.4.6)
• Chapter 12. A proof of equation (8.4.8)
• Chapter 13. A proof of equation (8.4.7)
• Chapter 14. The integration by parts formula
• Chapter 15. The hypoelliptic estimates
• Chapter 16. Harmonic oscillator and the J0 function
• Chapter 17. The limit of A'2φb,±H as b → 0
• Bibliography
• Subject Index
• Index of Notation