On generalized measure contraction property and energy functionals over Lipschitz maps

We construct Sobolev spaces and energy functionals over maps between metric spaces under the strong measure contraction property of Bishop-Gromov type, which is a generalized notion of Ricci curvature bounded below. We also present the notion of generalized measure contraction property, which gives a characterization of energies by approximating energies of Sturm type over Lipschitz maps.