Displaying similar documents to “Note on pull-back and Lelong number of currents”

On envelopes of holomorphy of domains covered by Levi-flat hats and the reflection principle

Joël Merker (2002)

Annales de l’institut Fourier

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In the present paper, we associate the techniques of the Lewy-Pinchuk reflection principle with the Behnke-Sommer continuity principle. Extending a so-called to a parameterized congruence of Segre varieties, we are led to studying the envelope of holomorphy of a certain domain covered by a smooth Levi-flat “hat”. In our main theorem, we show that every 𝒞 ∞ -smooth CR diffeomorphism h : M → M ' between two globally minimal real analytic hypersurfaces in ℂ n ( n ≥ 2 ) is real analytic at every point of M ...

An approximation theorem related to good compact sets in the sense of Martineau

Jean-Pierre Rosay, Edgar Lee Stout (2000)

Annales de l'institut Fourier

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This note contains an approximation theorem that implies that every compact subset of ℂ n is a good compact set in the sense of Martineau. The property in question is fundamental for the extension of analytic functionals. The approximation theorem depends on a finiteness result about certain polynomially convex hulls.

Brolin's theorem for curves in two complex dimensions

Charles Favre, Mattias Jonsson (2003)

Annales de l’institut Fourier

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Given a holomorphic mapping f : ℙ 2 → ℙ 2 of degree d ≥ 2 we give sufficient conditions on a positive closed (1,1) current of S of unit mass under which d - n f n * S converges to the Green current as n → ∞ . We also conjecture necessary condition for the same convergence.