|ISSN 1088-6826(online) ISSN 0002-9939(print)|
A holomorphic function with wild boundary behavior
Abstract: Let be the open unit ball in . It is known that if is a function holomorphic in , then there are and an arc in , with as one endpoint along which is constant. We prove
Theorem. There exist an and a function holomorphic in with the property that, if and is a path with as one endpoint, such that is contained in the open ball of radius which is contained in and tangent to at , then does not exist.
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