Displaying similar documents to “Brolin's theorem for curves in two complex dimensions”

Determination of the pluripolar hull of graphs of certain holomorphic functions

Armen Edigarian, Jan Wiegerinck (2004)

Annales de l’institut Fourier

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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.

Approximation of holomorphic functions of infinitely many variables II

László Lempert (2000)

Annales de l'institut Fourier

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Let X be a Banach space and B ( R ) ⊂ X the ball of radius R centered at 0 . Can any holomorphic function on B ( R ) be approximated by entire functions, uniformly on smaller balls B ( r ) ? We answer this question in the affirmative for a large class of Banach spaces.

On vanishing inflection points of plane curves

Mauricio Garay (2002)

Annales de l’institut Fourier

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We study the local behaviour of inflection points of families of plane curves in the projective plane. We develop normal forms and versal deformation concepts for holomorphic function germs f : ( ℂ 2 , 0 ) ⟶ ( ℂ , 0 ) which take into account the inflection points of the fibres of f . We give a classification of such function- germs which is a projective analog of Arnold’s A,D,E classification. We compute the versal deformation with respect to inflections of Morse function-germs.

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.

Vector fields, invariant varieties and linear systems

Jorge Vitório Pereira (2001)

Annales de l’institut Fourier

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We investigate the interplay between invariant varieties of vector fields and the inflection locus of linear systems with respect to the vector field. Among the consequences of such investigation we obtain a computational criterion for the existence of rational first integrals of a given degree, bounds for the number of first integrals on families of vector fields, and a generalization of Darboux's criteria. We also provide a new proof of Gomez--Mont's result...