Quasiconformal Mappings and Curvatures on Metric Measure Spaces

Abstract: In an attempt to develop higher-dimensional quasiconformal mappings on metric measure spaces with curvature conditions, i.e. from Ahlfors to Alexsandrov, we show that a non-collapsed $\mathrm{RCD}(0,n)$ space ($n\geq2$) with Euclidean growth volume is an $n$-Loewner space and satisfies the infinitesimal-to-global principle.