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

The notion of the metric measure foliation was introduced by Galaz-García, Kell, Mondino, and Sosa in [9]. 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.

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The author was supported by JSPS KAKENHI Grant Number 17J02121.

Received 27 October 2018

Accepted 10 December 2019

Published 26 April 2023