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 Alexandrov, we show that for n≥2 a noncollapsed RCD(0,n) space with Euclidean volume growth is an n-Loewner space and satisfies the infinitesimal-to-global principle.

Keywords

• quasiconformal mapping
• quasi-symmetric
• rcd spaces
• infinitesimal-to-global principle