Displaying similar documents to “Real analytic maximum modulus manifolds in strictly pseudoconvex boundaries”

Maximum modulus sets

Thomas Duchamp, Edgar Lee Stout (1981)

Annales de l'institut Fourier

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We investigate some aspects of maximum modulus sets in the boundary of a strictly pseudoconvex domain D of dimension N . If Σ ⊂ b D is a smooth manifold of dimension N and a maximum modulus set, then it admits a unique foliation by compact interpolation manifolds. There is a semiglobal converse in the real analytic case. Two functions in A 2 ( D ) with the same smooth N -dimensional maximum modulus set are analytically related and are polynomially related if a certain homology class in H 1 ( D , R ) vanishes or...

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.

CR submanifolds of maximal CR dimension in complex manifolds

Mirjana Djorić, Masafumi Okumura (2002)

Banach Center Publications

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The aim of this paper is to investigate n-dimensional real submanifolds of complex manifolds in the case when the maximal holomorphic tangent space is (n-1)-dimensional. In particular, we give some examples and we consider the Levi form on these submanifolds, especially when the ambient space is a complex space form. Moreover, we show that on some remarkable class of real hypersurfaces of complex space forms, the Levi form cannot vanish identically.