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Maximum modulus sets and reflection sets. (English) Zbl 0725.32007
We study sets in the boundary of a domain in \({\mathbb{C}}^ n\), on which a holomorphic function has maximum modulus. In particular we show that in a real analytic strictly pseudoconvex boundary, maximum modulus sets of maximum dimension are real analytic. Maximum modulus sets are related to “reflection sets”, which are sets along which appropriate collections of holomorphic and antiholomorphic functions agree.

MSC:
32A40 Boundary behavior of holomorphic functions of several complex variables
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