Combinatorial harmonic maps and discrete-group actions on Hadamard spaces
arXiv:math/0410019
Abstract
We use the combinatorial harmonic map theory to study the isometric actions of discrete groups on Hadamard spaces. Given a finitely generated group acting by automorphisms, properly discontinuously and cofinitely on a simplicial complex and its isometric action on a Hadamard space, we formulate criterions for the action to have a global fixed point.
39 pages, 3 figures, to appear in Geometriae Dedicata