Locally homogeneous RCD spaces

Abstract

The goal of this note is to demonstrate how existing results can be adapted to establish the following result: A locally metric measure homogeneous $\mathrm{RCD}(K,N)$ space is isometric to, after multiplying a positive constant to the reference measure, a smooth Riemannian manifold with the Riemannian volume measure.

23 pages, to appear in Springer Tohoku Series in Mathematics