Extensions of bounded holomorphic functions on the tridisk

A set V in the tridisk D-3 has the polynomial extension property if for every polynomial p there is a function phi on D-3 so that parallel to phi parallel to(D3) = parallel to p parallel to(V) and phi vertical bar(V) = p vertical bar(V). We study sets V that are relatively polynomially convex and have the polynomial extension property. If V is one-dimensional, and is either algebraic, or has polynomially convex projections, we show that it is a retract. If V is two-dimensional, we show that either it is a retract, or, for any choice of the coordinate functions, it is the graph of a function of two variables.