Displaying similar documents to “Maximum modulus sets”

Maximum modulus sets and reflection sets

Alexander Nagel, Jean-Pierre Rosay (1991)

Annales de l'institut Fourier

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We study sets in the boundary of a domain in 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 , which are sets along which appropriate collections of holomorphic and antiholomorphic functions agree.

Finitely generated ideals in A ( ω )

John Erik Fornaess, M. Ovrelid (1983)

Annales de l'institut Fourier

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The Gleason problem is solved on real analytic pseudoconvex domains in C 2 . In this case the weakly pseudoconvex points can be a two-dimensional subset of the boundary. To reduce the Gleason problem to a ∂ ‾ question it is shown that the set of Kohn-Nirenberg points is at most one-dimensional. In fact, except for a one-dimensional subset, the weakly pseudoconvex boundary points are R -points as studied by Range and therefore allow local sup-norm estimates for ∂ ‾ .