Rigidity and regularity for almost homogeneous spaces with Ricci curvature bounds

Xin Qian

We say that a metric space $X$ is $(\hat{I}\mu ,G)$-homogeneous if $G<Iso(X)$ is a discrete group of isometries with $diam(X/G)<\hat{I}\mu$.\ A sequence of $(\hat{I}{\mu }_i,G_i)$-homogeneous spaces $X_i$ wit…