Let X n = {X 1 ,. .. , X n } ⊂ R D be an iid sample drawn with a unknown distribution P X associated to a density f and supported by S. We study the problem of estimating the density f. When the density is continuous with regard to the Lebesgue measure and under wide hypotheses, the proposed density estimator has a minimax local asymptotic behaviour when D ≤ 7, but also offers global warranties (whatever the dimension is). It allows to estimate the level sets of the density consistently, even for level sets that intersects the boundary. It is also easy to adapt it to the case of a distribution supported by a d-dimensional, smooth enough, sub-manifold of R D with similar convergence rates (depending on d instead of D). The paper is dedicated to the study of the asymptotical behaviour of the proposed estimator based on local behaviour and is concluded by numerical experiments.