Geometric wave propagator on Riemannian manifolds

Capoferri, M., Levitin, M. ORCID: https://orcid.org/0000-0003-0020-3265 and Vassiliev, D. (2022) Geometric wave propagator on Riemannian manifolds. Communications in Analysis and Geometry, 30 (8). pp. 1713-1777. ISSN 1944-9992 doi: 10.4310/CAG.2022.v30.n8.a2

Abstract/Summary

We study the propagator of the wave equation on a closed Riemannian manifold M. We propose a geometric approach to the construction of the propagator as a single oscillatory integral global both in space and in time with a distinguished complex-valued phase function. This enables us to provide a global invariant definition of the full symbol of the propagator - a scalar function on the cotangent bundle - and an algorithm for the explicit calculation of its homogeneous components. The central part of the paper is devoted to the detailed analysis of the subprincipal symbol; in particular, we derive its explicit small time asymptotic expansion. We present a general geometric construction that allows one to visualise topological obstructions and describe their circumvention with the use of a complex-valued phase function. We illustrate the general framework with explicit examples in dimension two.

Item Type	Article
URI	https://reading-clone.eprints-hosting.org/id/eprint/89447
Identification Number/DOI	10.4310/CAG.2022.v30.n8.a2
Refereed	Yes
Divisions	Science > School of Mathematical, Physical and Computational Sciences > Department of Mathematics and Statistics
Publisher	International Press
Download/View statistics	View download statistics for this item