Einstein gravity on the codimension 2 brane?

We look at general brane worlds in six-dimensional Einstein-Gauss-Bonnet gravity. We find the general matching conditions for the brane world, which remarkably give precisely the four-dimensional Einstein equations for the brane, even when the extra dimensions are noncompact and have infinite volume. Relaxing regularity of the curvature in the vicinity of the brane, or having a thick brane, gives rise to an additional term containing information on the brane's embedding in the bulk. We comment on the relevance of these results to a possible solution of the cosmological constant problem.