Global parametrices and dispersive estimates for variable coefficient wave equations

Abstract

In this article we consider variable coefficient, time-dependent wave equations. Using phase space methods we construct outgoing parametrices and prove Strichartz-type estimates globally in time. This is done in the context of C^2 metrics which satisfy a weak aymptotic flatness condition at infinity.

52 pages. Several typos corrected, and the exposition was expanded in Sections 8 and beyond