The analogous problem of describing the polynomial hull of a compact set fibered over the unit circle Γ in C has been studied in [1; 3; 8; 9; 11]. A major issue in all of these works is to describe the extent of analytic structure—that is, when there exist analytic varieties contained in the polynomial hull with boundary contained in Y. One reason for this is that discovering such a variety in Y explains why the points on that variety lie in Y by virtue of the well-known local maximum modulus principle on analytic varieties. In this work, we shall examine when one can expect a higher degree of analytic structure, that is, when there exist analytic manifolds of dimension 2 in Y with boundary in Y. In particular, we shall examine when such an analytic manifold is in fact the graph of an analytic function over B_2.
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