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Transactions of the American Mathematical Society

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On the existence of global Tchebychev nets


Authors: Sandra L. Samelson and W. P. Dayawansa
Journal: Trans. Amer. Math. Soc. 347 (1995), 651-660
MSC: Primary 53C22; Secondary 53C21, 58G30
MathSciNet review: 1233983
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Abstract: Let $ S$ be a complete, open simply connected surface. Suppose that the integral of the Gauss curvature over arbitrary measurable sets is less than $ \pi /2$ in magnitude. We show that the surface admits a global Tchebychev net.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1995-1233983-3
Keywords: Tchebychev nets, curvature bounds
Article copyright: © Copyright 1995 American Mathematical Society