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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
Received: 13.11.1984

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}


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