Some generalizations of Chirka's extension theorem

In this paper, we generalize Chirka's theorem on the extension of functions holomorphic in a neighbourhood of - where is the open unit disc in and is the graph of a continuous valued function on - to higher dimensions, for certain classes of graphs . In particular, we show that Chirka's extension theorem generalizes to configurations in , involving graphs of (non-holomorphic) polynomial maps with small coefficients.