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 Mat. Sb. (N.S.), 1981, Volume 116(158), Number 4(12), Pages 558–567 (Mi msb2484)

Bounded complete weakly nonregular surfaces with negative curvature bounded away from zero

È. R. Rozendorn

Abstract: In three-dimensional Euclidean space we construct a bounded saddle surface of class $C^1$, complete in its intrinsic metric. This surface has $C^\infty$ regularity everywhere except for a countable set of singular points (saddle points of the third order, isolated in the intrinsic metric). The Gaussian curvature in the sense of A. D. Aleksandrov is defined on the whole surface, is continuous and differentiable, and satisfies the inequality $K\leqslant-1$.
Bibliography: 10 titles.

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English version:
Mathematics of the USSR-Sbornik, 1983, 44:4, 501–509

Bibliographic databases:

UDC: 513.735
MSC: 53A05

Citation: È. R. Rozendorn, “Bounded complete weakly nonregular surfaces with negative curvature bounded away from zero”, Mat. Sb. (N.S.), 116(158):4(12) (1981), 558–567; Math. USSR-Sb., 44:4 (1983), 501–509

Citation in format AMSBIB
\Bibitem{Roz81}
\by \`E.~R.~Rozendorn
\paper Bounded complete weakly nonregular surfaces with negative curvature bounded away from zero
\jour Mat. Sb. (N.S.)
\yr 1981
\vol 116(158)
\issue 4(12)
\pages 558--567
\mathnet{http://mi.mathnet.ru/msb2484}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=665856}
\zmath{https://zbmath.org/?q=an:0507.53001|0477.53003}
\transl
\jour Math. USSR-Sb.
\yr 1983
\vol 44
\issue 4
\pages 501--509
\crossref{https://doi.org/10.1070/SM1983v044n04ABEH000982}

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This publication is cited in the following articles:
1. P. E. Bradley, N. Paul, “Using the Relational Model to Capture Topological Information of Spaces”, Computer J, 2009
2. Connell Ch. Ullman J., “Ends of Negatively Curved Surfaces in Euclidean Space”, Manuscr. Math., 131:3-4 (2010), 275–303
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