| Description |
1 online resource (viii, 367 pages) : illustrations |
| Series |
Annals of mathematics studies ; no. 167 |
|
Annals of mathematics studies ; no. 167.
|
| Contents |
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? +8 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 metricsChapter 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 J[sub(0)] function; Chapter 17. The limit of [omitt |
| Summary |
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 Gilles Lebeau establish the basic functional analytic properties of this operator, which is also studied from the perspective of local index theory and analytic torsion. The book shows that the hypoelliptic Laplacian provides a geometric version of the Fokker-Planck equations. The authors give th |
| Bibliography |
Includes bibliographical references (pages 353-357) and indexes |
| Notes |
In English |
|
Print version record |
| Subject |
Differential equations, Hypoelliptic.
|
|
Laplacian operator.
|
|
Metric spaces.
|
|
MATHEMATICS -- Functional Analysis.
|
|
MATHEMATICS -- Geometry -- General.
|
|
Differential equations, Hypoelliptic
|
|
Laplacian operator
|
|
Metric spaces
|
|
Hodge-Theorie
|
|
Hypoelliptischer Operator
|
|
Laplace-Operator
|
|
Elliptische differentiaalvergelijkingen.
|
|
Laplace-operatoren.
|
|
Metrische ruimten.
|
|
Partiële differentiaalvergelijkingen.
|
|
Tweede orde.
|
| Form |
Electronic book
|
| Author |
Lebeau, Gilles.
|
| LC no. |
2008062103 |
| ISBN |
9781400829064 |
|
1400829062 |
|
9786612458378 |
|
6612458372 |
|
