The wave kernel on asymptotically complex hyperbolic manifolds

Abstract

We study the behavior of the wave kernel of the Laplacian on asymptotically complex hyperbolic manifolds for finite times. We show that the wave kernel on such manifolds belongs to an appropriate class of Fourier integral operators and analyze its trace. This construction proves that the singularities of its trace are contained in the set of lengths of closed geodesics and we obtain an asymptotic expansion for the trace at time zero.