Abstract
  In this joint work with M. Keel & H. Smith we prove that the global existence theorem of Christodoulou and
Klainerman for quasilinear wave equations satisfying the null condition holds in the setting of Dirichlet-
wave equations outside of star-shaped obstacles.  We use an adaptation of Christodoulou's conformal method.
The main ingredients are an energy estimate that is related to classical decay estimates of Morawetz and also a
pointwise estimate that is related to recent global Strichartz estimates obtained by Hart Smith and the speaker.