The Hypoelliptic Laplacian and Ray-Singer Metrics. (AM-167) /

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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Detalles Bibliográficos
Autor principal: Bismut, Jean-Michel
Otros Autores: Lebeau, Gilles
Formato: Electrónico eBook
Idioma:Inglés
Publicado: Princeton : Princeton University Press, 2008.
Colección:Book collections on Project MUSE.
Temas:
Tweede orde.
Partiële differentiaalvergelijkingen.
Metrische ruimten.
Laplace-operatoren.
Elliptische differentiaalvergelijkingen.
Laplace-Operator
Hypoelliptischer Operator
Hodge-Theorie
Metric spaces.
Laplacian operator.
Differential equations, Hypoelliptic.
MATHEMATICS > Geometry > General.
MATHEMATICS > Functional Analysis.
Espaces metriques.
Laplacien.
Équations differentielles hypo-elliptiques.
Electronic books.
Acceso en línea:Texto completo
Tabla de Contenidos:
  • 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.

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