The regular type of a real hyper-surface M in an (almost) complex manifold at some point p is the maximal contact order at p of M with germs of non singular (pseudo) holomorphic disks. The main purpose of this paper is to give two intrinsic characterizations the type : one in terms of Lie brackets of a complex tangent vector field on M, the other in terms of some kind of derivatives of the Levi form. Mathematics Subject Classification (2000): 32T25,32Q60The purpose of this paper is to study order of contact between holomorphic curves (as well pseudoholomorphic curves) and a real hyper-surface. In the integrable case, this invariant is connected to the boundary behavior of the Cauchy-Riemann equations, the Bergman kernel, invariant metrics, etc.. see for example [5,3,4,10,9]. One of the difficulty to use this number in function theory on a domain D, is due to the fact that in general, it was not known how to calculate it with intrinsic "complex geometry" of the boundary of D. In C 2 the situation is clear (see [9]) ; for C n (n > 2), we only know how to compute the order of contact of complex hyper-surface with the natural Lie algebra of the boundary of D (see [2]). In [2], I. Graham and T. Bloom ask how to characterize the regular "type" in a similar intrinsic way with only one complex vector field; T. Bloom (see [1]) succeeds in the pseudoconvex case in C 3 but unfortunately, the result is not valid without the pseudoconvexity hypothesis.In this article, we consider an hyper-surface (pseudoconvex or not) in C n or in R 2n endowed with an almost complex structure, and characterize its "regular one type", by means of Lie brackets of one "complex tangent vector field" on the hyper-surface (see theorem 1), and by means of derivatives of the "levi form" in

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Abstract. It is shown, that the so-called Blaschke condition characterizes in any bounded smooth convex domain of finite type exactly the divisors which are zero sets of functions of the Nevanlinna class on the domain. The main tool is a non-isotropic L 1 estimate for solutions of the Cauchy-Riemann equations on such domains, which are obtained by estimating suitable kernels of BerndtssonAndersson type. §1. Introduction and resultsIn their article [2] J. Bruna, Ph. Charpentier and Y. Dupain did a large step towards a complete characterization of the zero sets of the Nevanlinna class on all convex domains of finite type in C n . The purpose of this article is to complete their result.For the convenience of the reader we recall at first briefly the following definitions and facts:If D ⊂⊂ C n is a C ∞ -smoothly bounded domain and ρ a smooth defining function for D, then the Nevanlinna class N (D) isHere ∂D ε = {z : ρ(z) = −ε} for ε > 0 small enough and dσ ε (z) denotes the Euclidean surface measure on ∂D ε . Furthermore, if X ⊂ D is a complex analytic hypersurface with irreducible decomposition

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