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Convex Hulls in Singular Spaces of Negative Curvature |
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| Authors: | Christoph Hummel Urs Lang Viktor Schroeder |
| Institution: | (1) Departement Mathematik, ETH Zentrum, Rämistr. 101, CH-8092 Zürich, Switzerland. e-mail;(2) Departement Mathematik, ETH Zentrum, Rämistr. 101, CH-8092 Zürich, Switzerland. e-mail;(3) Institut für Mathematik, Universität Zürich, Winterthurer Str. 190, CH-8057 Zürich, Switzerland. e-mail |
| Abstract: | 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 . |
| Keywords: | Alexandrov spaces almost convex convex hulls negative curvature |
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