Gh-convergence of CAT(0)-spaces: stability of the Euclidean factor

Abstract

We prove that if a sequence of geodesically complete CAT(0)-spaces $$X_j$$ X j with uniformly cocompact discrete groups of isometries converges in the Gromov-Hausdorff sense to $$X_\infty $$ X ∞ , then the dimension of the maximal Euclidean factor splitted off by $$X_\infty $$ X ∞ and $$X_j$$ X j is the same, for j big enough. In other words, no additional Euclidean factors can appear in the limit.