Abstract
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.
Original language | English (US) |
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Pages (from-to) | 163-186 |
Number of pages | 24 |
Journal | Mathematics of the USSR - Sbornik |
Volume | 56 |
Issue number | 1 |
DOIs | |
State | Published - Feb 28 1987 |
All Science Journal Classification (ASJC) codes
- General Mathematics