%0 Journal Article
%T The continuity equation on metric measure spaces
%A Nicola Gigli
%A Bangxian Han
%J Mathematics
%D 2014
%I arXiv
%X Aim of this paper is to show that it makes sense to write the continuity equation on a metric measure space $(X,d,m)$ and that absolutely continuous curves $\mu_t$ w.r.t. the distance $W_2$ can be completely characterized as solutions of the continuity equation itself, provided we impose the condition $\mu_t\leq Cm$ for every $t$ and some $C>0$.
%U http://arxiv.org/abs/1406.6350v1