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-García, 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.

The fiber control condition in the first version has been revised to the metric measure foliation because these conditions are actually equivalent