CAT(0) spaces without linear filling at the asymptotic rank

Abstract

For every integer $\nu \ge 2$, we construct a $(\nu +1)$-dimensional, locally compact, geodesically complete CAT(0) space of asymptotic rank $\nu$ which does not satisfy a linear isoperimetric inequality for integral $\nu$-cycles. Its filling function is bounded below by $cv\log v$ for all sufficiently large $v$.