  The present paper is devoted to semigroups of nonexpansive mappings on metric
spaces of nonpositive curvature. We show that the Mosco convergence of a
sequence of convex lsc functions implies convergence of the corresponding
resolvents and convergence of the gradient flow semigroups. This extends the
classical results of Attouch, Brezis and Pazy into spaces with no linear
structure. The same method can be further used to show the convergence of
semigroups on a sequence of spaces, which solves a problem of [Kuwae and
Shioya, Trans. Amer. Math. Soc., 2008].
