### 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 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.

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 |

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### All Science Journal Classification (ASJC) codes

- Mathematics(all)

### Cite this

*Mathematics of the USSR - Sbornik*,

*56*(1), 163-186. https://doi.org/10.1070/SM1987v056n01ABEH003030

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*Mathematics of the USSR - Sbornik*, vol. 56, no. 1, pp. 163-186. https://doi.org/10.1070/SM1987v056n01ABEH003030

**Three-dimensional manifolds of nonnegative ricci curvature, with boundary.** / Ananov, N. G.; Burago, Yury D.; Zalgaller, V. A.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Three-dimensional manifolds of nonnegative ricci curvature, with boundary

AU - Ananov, N. G.

AU - Burago, Yury D.

AU - Zalgaller, V. A.

PY - 1987/2/28

Y1 - 1987/2/28

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=84956134578&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84956134578&partnerID=8YFLogxK

U2 - 10.1070/SM1987v056n01ABEH003030

DO - 10.1070/SM1987v056n01ABEH003030

M3 - Article

AN - SCOPUS:84956134578

VL - 56

SP - 163

EP - 186

JO - Sbornik Mathematics

JF - Sbornik Mathematics

SN - 1064-5616

IS - 1

ER -