Rank-one isometries of proper CAT(0)-spaces

Details Rank-one isometries of proper CAT(0)-spaces Rank-one isometries of proper CAT(0)-spaces

2008-10-21

arxiv.org/abs/0810.3794v2

Mathematics

Metric Geometry

Several corrections; to appear in Contemp. Math

Scientific paper

Let G be a non-elementary group of isometries of a proper CAT(0)-space with limit set L. We survey properties of the action of G on L under the assumption that G contains a rank-one element. Among others, we show that there is a dense orbit for the action of G on the complement of the diagonal in LxL and that pairs of fixed points of rank-one elements are dense in the complement of the diagonal of LxL.

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