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Abstract
We prove that if is a holomorphic map of the unit ball such that df(0) =I and f(B
n
) is convex, then any translation of f(B
n
) through a distance less than π/2 meets f(B
n
). In contrast to the one-variable situation (studied by MacGregor), the result is not true if the convexity assumption is dropped completely.
AMS No. 32H02
∗Partially supported by the Natural Sciences and Engineering Research Council of Canada under Grant A9221.
∗∗Partially supported by NSERC Undergraduate Summer Research Award.
∗Partially supported by the Natural Sciences and Engineering Research Council of Canada under Grant A9221.
∗∗Partially supported by NSERC Undergraduate Summer Research Award.
Notes
∗Partially supported by the Natural Sciences and Engineering Research Council of Canada under Grant A9221.
∗∗Partially supported by NSERC Undergraduate Summer Research Award.