an:04196381
Zbl 0725.32007
Nagel, Alexander; Rosay, Jean-Pierre
Maximum modulus sets and reflection sets
EN
Ann. Inst. Fourier 41, No. 2, 431-466 (1991).
00007576
1991
j
32A40
maximum modulus sets
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.
A.Nagel and J.-P.Rosay