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The paper gives a simple example of a complete CAT(–1)-space containing a set S with the following property: the boundary at infinity ∂ ∞CH(S)of the convex hull of S differs from S by an isolated point. In contrast to this it is shown that if S is a union of finitely many convex subsets of a complete CAT(–1)-space X, then ∂ ∞CH(S) = ∂ ∞ S. Moreover, this identity holds without restrictions on S if CH is replaced by some notion of 'almost convex hull'.
|Item Type:||Journal Article, refereed, original work|
|Communities & Collections:||07 Faculty of Science > Institute of Mathematics|
|Uncontrolled Keywords:||Alexandrov space; almost convex; convex hull; negative curvature|
|Deposited On:||29 Nov 2010 17:27|
|Last Modified:||28 Nov 2013 03:03|
|Citations:||Web of Science®. Times cited: 4|
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