Conformal transformation on metric measure spaces

Abstract

We study several problems concerning conformal transformation on metric measure spaces, including the Sobolev space, the differential structure and the curvature-dimension condition under conformal transformations. This is the first result about preservation of lower curvature bounds under perturbation, which is new even on Alexandrov spaces.

arXiv commentarXiv admin note: text overlap with arXiv:1412.0441