The hypoelliptic Laplacian and Ray-Singer metrics /
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...
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| Định dạng: | Licensed eBooks |
| Ngôn ngữ: | Tiếng Anh |
| Được phát hành: |
Princeton :
Princeton University Press,
2008.
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| Loạt: | Annals of mathematics studies ;
no. 167. |
| Truy cập trực tuyến: | https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=305771 |
Mục lục:
- 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.