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 ≥ 0 and Ric ≥ -min H2) 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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