Displaying similar documents to “An approximation theorem related to good compact sets in the sense of Martineau”

Determination of the pluripolar hull of graphs of certain holomorphic functions

Armen Edigarian, Jan Wiegerinck (2004)

Annales de l’institut Fourier

Similarity:

Let A be a closed polar subset of a domain D in ℂ . We give a complete description of the pluripolar hull Γ D × ℂ * of the graph Γ of a holomorphic function defined on D ∖ A . To achieve this, we prove for pluriharmonic measure certain semi-continuity properties and a localization principle.

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

Joël Merker (2002)

Annales de l’institut Fourier

Similarity:

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 ...

Brolin's theorem for curves in two complex dimensions

Charles Favre, Mattias Jonsson (2003)

Annales de l’institut Fourier

Similarity:

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.