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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Construction of convex sets in negatively curved manifolds


Author: Albert Borbély
Journal: Proc. Amer. Math. Soc. 118 (1993), 205-210
MSC: Primary 53C20
MathSciNet review: 1166353
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Abstract: It was proved by Choi that one can solve the Dirichlet problem at infinity for simply connected negatively curved manifolds by constructing appropriate convex sets. All the known constructions, it seems, inherently need some kind of growth condition on the curvature; therefore, it is interesting to find new ways to construct convex sets in negatively curved manifolds. In this paper we give a new way to construct convex sets from sets we call $ \varepsilon $-almost-convex. From the point of view of this problem this can be considered as a natural generalization of convexity.


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DOI: http://dx.doi.org/10.1090/S0002-9939-1993-1166353-0
PII: S 0002-9939(1993)1166353-0
Article copyright: © Copyright 1993 American Mathematical Society