On Fixed Points and Uniformly Convex Spaces
نویسنده
چکیده
The purpose of this note is to present two elementary, but useful, facts concerning actions on uniformly convex spaces. We demonstrate how each of them can be used in an alternative proof of the triviality of the first Lp-cohomology of higher rank simple Lie groups, proved in [1]. Let G be a locally compact group with a compact generating set K ∋ 1, and let X be a complete Busemann non-positively curved uniformly convex metric space. Suppose that G acts continuously by isometries on X such that the displacement goes to infinity, i.e. dK(x) = max k∈K d(x, k · x) → ∞ when x → ∞,
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