Convergence of energy functionals and stability of lower bounds of Ricci curvature via metric measure foliation

Abstract

The notion of the metric measure foliation is introduced by Galaz-Garcia, Kell, Mondino, and Sosa. They studied the relation between a metric measure space with a metric measure foliation and its quotient space. They showed that the curvature-dimension condition and the Cheeger energy functional preserve from a such space to its quotient space. Via the metric measure foliation, we investigate the convergence theory for a sequence of metric measure spaces whose dimensions are unbounded.