The wave kernel on asymptotically complex hyperbolic manifolds

  • Hadrian Quan

    University of California, Santa Cruz, USA
The wave kernel on asymptotically complex hyperbolic manifolds cover
Download PDF

This article is published open access under our Subscribe to Open model.

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.

Cite this article

Hadrian Quan, The wave kernel on asymptotically complex hyperbolic manifolds. J. Spectr. Theory 15 (2025), no. 2, pp. 533–562

DOI 10.4171/JST/562