*Accepted Paper*

**Inserted:** 27 mar 2009

**Last Updated:** 8 oct 2013

**Journal:** Ann. Mat. Pura Appl.

**Year:** 2010

**Abstract:**

Given a metric space $X$, we consider a class of action functionals, generalizing those considered in Brancolini-Buttazzo-Santambrogio (J. Eur. Math. Soc. 8 (2006)) and Ambrosio-Santambrogio (Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. Rend. Lincei -- Mat. Appl. 18 (2007)), which measure the cost of joining two given points $x_0$ and $x_1$, by means of an absolutely continuous curve. In the case $X$ is given by a space of probability measures, we can think of these action functionals as giving the cost of some congested*concentrated mass transfer problem. We focus on the possibility to split the mass in its {\it moving part} and its part that (in some sense) has already reached its final destination: we consider new action functionals, taking into account only the contribution of the moving part.*

**Keywords:**
Analysis in metric spaces, Minimizing curves, Branching transport

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