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Transactions of the American Mathematical Society

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Convexity of the ideal boundary for complete open surfaces

Author: Jin-Whan Yim
Journal: Trans. Amer. Math. Soc. 347 (1995), 687-700
MSC: Primary 53C20; Secondary 53C45
MathSciNet review: 1243176
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Abstract: For complete open surfaces admitting total curvature, we define several kinds of convexity for the ideal boundary, and provide examples of each of them. We also prove that a surface with most strongly convex ideal boundary is in fact a generalization of a Hadamard manifold in the sense that the ideal boundary consists entirely of Busemann functions.

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Article copyright: © Copyright 1995 American Mathematical Society