  The global characteristic initial value problem for linear wave equations on
globally hyperbolic Lorentzian manifolds is examined, for a class of smooth
initial value hypersurfaces satisfying favourable global properties. First it
is shown that, if geometrically well-motivated restrictions are placed on the
supports of the (smooth) initial datum and of the (smooth) inhomogeneous term,
then there exists a continuous global solution which is smooth "on each side"
of the initial value hypersurface. A uniqueness result in Sobolev regularity
$H^{1/2+\varepsilon}_\mathrm{loc}$ is proved among solutions supported in the
union of the causal past and future of the initial value hypersurface, and
whose product with the indicator function of the causal future (resp. past) of
the hypersurface is past compact (resp. future compact). An explicit
representation formula for solutions is obtained, which prominently features an
invariantly defined, densitised version of the null expansion of the
hypersurface. Finally, applications to quantum field theory on curved
spacetimes are briefly discussed.
