Geodesic
Three-dimensional manifolds of nonnegative Ricci curvature, with boundary
Sbornik. Mathematics, Tome 56 (1987) no. 1, pp. 163-186 
N. G. Ananov; Yu. D. Burago; V. A. Zalgaller. Three-dimensional manifolds of nonnegative Ricci curvature, with boundary. Sbornik. Mathematics, Tome 56 (1987) no. 1, pp. 163-186. http://geodesic.mathdoc.fr/item/SM_1987_56_1_a10/
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Voir la notice de l'article provenant de la source Math-Net.Ru

A complete proof is given of the theorem, announced earlier, that a three-dimensional Riemannian manifold with nonnegative Ricci curvature and nonempty connected boundary of nonnegative mean curvature (or, more generally, with $H\geqslant0$ and $\operatorname{Ric}\geqslant-\min H^2$) is a handlebody (oriented or nonoriented). The proof uses the fact that subanalytic sets have finite triangulations and a generalized limit angle lemma; these enable one to control the reconstruction of the equidistants of the boundary. Figures: 3. Bibliography: 27 titles.

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