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Determination of the pluripolar hull of graphs of certain holomorphic functions

Armen Edigarian, Jan Wiegerinck (2004)

Annales de l’institut Fourier

Let A be a closed polar subset of a domain D in . We give a complete description of the pluripolar hull Γ D × * 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.

Disc formulas for the weighted Siciak-Zahariuta extremal function

Benedikt Steinar Magnússon, Ragnar Sigurdsson (2007)

Annales Polonici Mathematici

We prove a disc formula for the weighted Siciak-Zahariuta extremal function V X , q for an upper semicontinuous function q on an open connected subset X in ℂⁿ. This function is also known as the weighted Green function with logarithmic pole at infinity and weighted global extremal function.

Disc functionals and Siciak-Zaharyuta extremal functions on singular varieties

Barbara Drinovec Drnovšek, Franc Forstnerič (2012)

Annales Polonici Mathematici

We establish plurisubharmonicity of envelopes of certain classical disc functionals on locally irreducible complex spaces, thereby generalizing the corresponding results for complex manifolds. We also find new formulae expressing the Siciak-Zaharyuta extremal function of an open set in a locally irreducible affine algebraic variety as the envelope of certain disc functionals, similarly to what has been done for open sets in ℂⁿ by Lempert and by Lárusson and Sigurdsson.

Distribution of nodes on algebraic curves in N

Thomas Bloom, Norman Levenberg (2003)

Annales de l’institut Fourier

Given an irreducible algebraic curves A in N , let m d be the dimension of the complex vector space of all holomorphic polynomials of degree at most d restricted to A . Let K be a nonpolar compact subset of A , and for each d = 1 , 2 , . . . , choose m d points { A d j } j = 1 , . . . , m d in K . Finally, let Λ d be the d -th Lebesgue constant of the array { A d j } ; i.e., Λ d is the operator norm of the Lagrange interpolation operator L d acting on C ( K ) , where L d ( f ) is the Lagrange interpolating polynomial for f of degree d at the points { A d j } j = 1 , . . . , m d . Using techniques of pluripotential...

Dynamics of meromorphic maps with small topological degree III: geometric currents and ergodic theory

Jeffrey Diller, Romain Dujardin, Vincent Guedj (2010)

Annales scientifiques de l'École Normale Supérieure

We continue our study of the dynamics of mappings with small topological degree on projective complex surfaces. Previously, under mild hypotheses, we have constructed an ergodic “equilibrium” measure for each such mapping. Here we study the dynamical properties of this measure in detail: we give optimal bounds for its Lyapunov exponents, prove that it has maximal entropy, and show that it has product structure in the natural extension. Under a natural further assumption, we show that saddle points...

Dynamics semi-conjugated to a subshift for some polynomial mappings in C2.

Gabriel Vigny (2007)

Publicacions Matemàtiques

We study the dynamics near infinity of polynomial mappings f in C2. We assume that f has indeterminacy points and is non constant on the line at infinity L∞. If L∞ is f-attracting, we decompose the Green current along itineraries defined by the indeterminacy points and their preimages. The symbolic dynamics that arises is a subshift on an infinite alphabet.

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