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Uniformization of small 3-orbifolds. (English. Abridged French version) Zbl 0976.57017
A 3-orbifold is called small if it has no essential 2-suborbifolds. In this note, the authors announce the uniformization of compact oriented small 3-orbifolds. Together with the uniformization of Haken 3-orbifolds [M. Boileau and J. Porti, Geometrization of 3-orbifolds of cyclic type, Astérisque 272 (2001)], this result implies the uniformization theorem for compact irreducible 3-orbifolds.
The proof if only sketched and details should appear elsewhere. More details are given in the case with finite fundamental group, which requires a different approach.

MSC:
57M50 General geometric structures on low-dimensional manifolds
57M60 Group actions on manifolds and cell complexes in low dimensions
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