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 Mat. Sb. (N.S.), 1985, Volume 128(170), Number 2(10), Pages 169–193 (Mi msb2122)

Three-dimensional manifolds of nonnegative Ricci curvature, with boundary

N. G. Ananov, Yu. D. Burago, V. A. Zalgaller

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 $H\geqslant0$ 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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English version:
Mathematics of the USSR-Sbornik, 1987, 56:1, 163–186

Bibliographic databases:

UDC: 514.76
MSC: Primary 53C20; Secondary 57R65

Citation: N. G. Ananov, Yu. D. Burago, V. A. Zalgaller, “Three-dimensional manifolds of nonnegative Ricci curvature, with boundary”, Mat. Sb. (N.S.), 128(170):2(10) (1985), 169–193; Math. USSR-Sb., 56:1 (1987), 163–186

Citation in format AMSBIB
\Bibitem{AnaBurZal85} \by N.~G.~Ananov, Yu.~D.~Burago, V.~A.~Zalgaller \paper Three-dimensional manifolds of nonnegative Ricci curvature, with boundary \jour Mat. Sb. (N.S.) \yr 1985 \vol 128(170) \issue 2(10) \pages 169--193 \mathnet{http://mi.mathnet.ru/msb2122} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=809484} \zmath{https://zbmath.org/?q=an:0612.53027|0596.53032} \transl \jour Math. USSR-Sb. \yr 1987 \vol 56 \issue 1 \pages 163--186 \crossref{https://doi.org/10.1070/SM1987v056n01ABEH003030}