THE HYPOELLIPTIC LAPLACIAN AND RAY-SINGER METRICS. (AM-167) by Jean-Michel Bismut, Gilles Lebeau ( 9780691137322 )

Item Details

Title:

THE HYPOELLIPTIC LAPLACIAN AND RAY-SINGER METRICS. (AM-167)

By:

Jean-Michel Bismut, Gilles Lebeau

Format:

Paperback

List price:

£65.00

Our price:

£52.00

Discount:

20% off

You save:

£13.00

ISBN 10:

0691137323

ISBN 13:

9780691137322

Availability:

Usually dispatched within 1-3 weeks.

Delivery rates

Stock:

Currently 0 available

Publisher:

PRINCETON UNIVERSITY PRESS

Pub. date:

18 August, 2008

Series:

Annals of Mathematics Studies

Pages:

376

Description:

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 the proper functional analytic setting in order to study this operator and develop a pseudodifferential calculus.

Synopsis:

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 the proper functional analytic setting in order to study this operator and develop a pseudodifferential calculus, which provides estimates on the hypoelliptic Laplacian's resolvent. When the deformation parameter tends to zero, the hypoelliptic Laplacian converges to the standard Hodge Laplacian of the base by a collapsing argument in which the fibers of the cotangent bundle collapse to a point. For the local index theory, small time asymptotics for the supertrace of the associated heat kernel are obtained. The Ray-Singer analytic torsion of the hypoelliptic Laplacian as well as the associated Ray-Singer metrics on the determinant of the cohomology are studied in an equivariant setting, resulting in a key comparison formula between the elliptic and hypoelliptic analytic torsions.

Illustrations:

4 line illus.

Publication:

Imprint:

Princeton University Press

Returns:

Returnable

Some other items by this author:

DIFFRACTION BY AN IMMERSED ELASTIC WEDGE (PB)

ELLIPTIC CARLEMAN ESTIMATES AND APPLICATIONS TO STABILIZATION AND CONTROLLABILITY, VOLUME I

ELLIPTIC CARLEMAN ESTIMATES AND APPLICATIONS TO STABILIZATION AND CONTROLLABILITY, VOLUME I (HB)

ELLIPTIC CARLEMAN ESTIMATES AND APPLICATIONS TO STABILIZATION AND CONTROLLABILITY, VOLUME II