Displaying similar documents to “Stability of the polynomial hull of T 2 ”

Proper holomorphic mappings between rigid polynomial domains in C.

Bernard Coupet, Nabil Ourimi (2001)

Publicacions Matemàtiques

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We describe the branch locus of proper holomorphic mappings between rigid polynomial domains in C. It appears, in particular, that it is controlled only by the first domain. As an application, we prove that proper holomorphic self-mappings between such domains are biholomorphic.

Some properties of Reinhardt domains

Le Mau Hai, Nguyen Quang Dieu, Nguyen Huu Tuyen (2003)

Annales Polonici Mathematici

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We first establish the equivalence between hyperconvexity of a fat bounded Reinhardt domain and the existence of a Stein neighbourhood basis of its closure. Next, we give a necessary and sufficient condition on a bounded Reinhardt domain D so that every holomorphic mapping from the punctured disk Δ * into D can be extended holomorphically to a map from Δ into D.

Extension and restriction of holomorphic functions

Klas Diederich, Emmanuel Mazzilli (1997)

Annales de l'institut Fourier

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Strong pathologies with respect to growth properties can occur for the extension of holomorphic functions from submanifolds D ' of pseudoconvex domains D to all of D even in quite simple situations; The spaces A p ( D ' ) : = 𝒪 ( D ' ) ∩ L p ( D ' ) are, in general, not at all preserved. Also the image of the Hilbert space A 2 ( D ) under the restriction to D ' can have a very strange structure.