On gluing Alexandrov spaces with lower Ricci curvature bounds

Abstract

In this paper we prove that in the class of metric measure space with Alexandrov curvature bounded from below the Riemannian curvature-dimension condition $RCD^*(K,N)$ with $K\in \mathbb{R}$ & $N\in [1,\infty)$ is preserved under doubling and gluing constructions provided the weight in the measure is semiconcave.