Maximum modulus sets

Thomas Duchamp; Edgar Lee Stout

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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.

On the boundary regularity of proper mappings

Franc Forstnerič (1986)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

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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 $\overline{\partial}$ 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 $\overline{\partial}$ .

Real analytic maximum modulus manifolds in strictly pseudoconvex boundaries

Andrei Iordan (1995)

Banach Center Publications

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Pseudoconvex domains over $q$ -complete manifolds

Viorel Vâjâitu (2000)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

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Holomorphic mapping of annuli in $C^{n}$ and the associated extremal function

Eric Bedford, Dan Burns (1979)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

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Displaying similar documents to “Maximum modulus sets”