Approximation des fonctions lisses sur certaines laminations

Details Approximation des fonctions lisses sur certaines laminations Approximation des fonctions lisses sur certaines laminations

2005-02-11

arxiv.org/abs/math/0502229v1

Mathematics

Complex Variables

Scientific paper

We show that on a Riemann surface lamination locally embedded in $\mathbb{C}^2$, $C^1$ functions (in the sense of the $C^1$ structure of the lamination) are uniform limits of ambient $C^1$ functions, with $L^p$ control on the derivatives along the leaves. This implies that locally in $C^2$, a (1,1) positive closed current dominated by a uniformly laminar current is itself uniformly laminar.

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