Boileau, Michel; Leeb, Bernhard; Porti, Joan Uniformization of small 3-orbifolds. (English. Abridged French version) Zbl 0976.57017 C. R. Acad. Sci., Paris, Sér. I, Math. 332, No. 1, 57-62 (2001). 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. Reviewer: Joan Porti (Bellaterra) Cited in 5 Documents MSC: 57M50 General geometric structures on low-dimensional manifolds 57M60 Group actions on manifolds and cell complexes in low dimensions Keywords:3-orbifold; small; geometric structure; uniformization PDFBibTeX XMLCite \textit{M. Boileau} et al., C. R. Acad. Sci., Paris, Sér. I, Math. 332, No. 1, 57--62 (2001; Zbl 0976.57017) Full Text: DOI