Mosco-convergence of Cheeger energies on varying spaces satisfying curvature dimension conditions

Abstract: We study the Mosco-convergence of Cheeger energies on Gromov-Hausdorff converging spaces satisfying different types of curvature dimension conditions. The case of functions of bounded variation is also considered. Our method, covering possibly infinite dimensional settings, is based on a Lagrangian approach and combines the stability properties of Wasserstein geodesics with the characterization of the nonsmooth calculus in duality with test plans.