We shall consider the
polynomially convex hull of the graph of a continuous complex-valued function on
the boundary of the unit ball. We show first that the hull covers the closed
unit ball and then consider several of its properties. In particular, when
is the hull also a graph; i.e. single sheeted? When the hull is a graph we
show, in some cases, that it contains analytic structure. We also consider
the graph in C2 of a real-valued continuous function on the boundary of a
3-cell which is contained in a real hyperplane in C2 and partially extend
some results of Bedford and Klingenberg who studied the case of smooth
functions.
