On the laminarity of certain currents. (Sur la laminarité de certains courants.) (French) Zbl 1061.32005

de Thélin, Henry

Ann. Sci. Éc. Norm. Supér. (4) 37, No. 2, 304-311 (2004).

The aim of this paper is the following theorem: Let \(C_n\) be a sequence of smooth analytic curves of the unit ball \(\mathbb B\subset\mathbb C^2\) (spreading a little beyond \(\overline{\mathbb B}\)). Let \(A_n\) be the area of \(C_n\), and \(G_n\) be the genus of \(C_n\). Suppose that the sequence of currents \(T_n=[C_n]/A_n\) converges toward a (1,1)-positive closed current \(T\) of \(\mathbb B\). If \(G_n = O(A_n)\), then \(T\) is laminar.

Reviewer: Vasily A. Chernecky (Odessa)

MSC:

32C30	Integration on analytic sets and spaces, currents
32C25	Analytic subsets and submanifolds

Keywords:

sequence of smooth analytic curves; lamination in a weak sense; laminar current; Ahlfors theory; majorization of the number of vertices; minorization of the number of edges

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