Polynomially convex hulls of graphs on the sphere

Abstract

Let Σ \Sigma be the graph of a continuous map of the unit sphere of C n \mathbb C^n into C m \mathbb C^m , and h ( Σ ) h(\Sigma ) the polynomially convex hull of Σ \Sigma . Several examples of h ( Σ ) h(\Sigma ) for n = m > 1 n=m>1 are given, which have different properties from the known ones for n > m n>m .