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The hypoelliptic Laplacian and Ray-Singer metrics

Author: Jean-Michel Bismut; Gilles Lebeau
Publisher: Princeton : Princeton University Press, 2008.
Series: Annals of mathematics studies, no. 167.
Edition/Format:   eBook : Document : EnglishView all editions and formats
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  Read more...
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Genre/Form: Electronic books
Additional Physical Format: Print version:
Bismut, Jean-Michel.
Hypoelliptic Laplacian and Ray-Singer metrics.
Princeton : Princeton University Press, 2008
(DLC) 2008062103
(OCoLC)213133468
Material Type: Document, Internet resource
Document Type: Internet Resource, Computer File
All Authors / Contributors: Jean-Michel Bismut; Gilles Lebeau
ISBN: 9781400829064 1400829062
OCLC Number: 593214464
Language Note: In English.
Description: 1 online resource (viii, 367 pages) : illustrations.
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.
Series Title: Annals of mathematics studies, no. 167.
Responsibility: Jean-Michel Bismut, Gilles Lebeau.

Abstract:

Presents the analytic foundations to the theory of the hypoelliptic Laplacian. This book shows that the hypoelliptic Laplacian provides a geometric version of the Fokker-Planck equations. It gives  Read more...

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