The authors Drove global existence of small solutions to a semilinear wave
equation outside of convex obstacles. This extends results of Christodoulou
and Klainerman who handled the Minkowski space version. The proof is a com
promise of the methods of Christodoulou and Klainerman. It relies on local
estimates proved earlier by Smith and Sogge together with classical energy
decay estimates for the wave equation of Morawetz, Lax and Phillips.