Convexity of the ideal boundary for complete open surfaces

Yim, Jin-Whan

doi:10.1090/S0002-9947-1995-1243176-1

Convexity of the ideal boundary for complete open surfaces
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by Jin-Whan Yim PDF

Trans. Amer. Math. Soc. 347 (1995), 687-700 Request permission

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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