Communications in Analysis and Geometry

Volume 30 (2022)

Number 6

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

Pages: 1301 – 1354



Daisuke Kazukawa (Mathematical Institute, Tohoku University, Sendai, Japan)


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.

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

Received 27 October 2018

Accepted 10 December 2019

Published 26 April 2023