On gluing Alexandrov spaces with lower Ricci curvature bounds

TL;DR

This paper demonstrates that the Riemannian curvature-dimension condition $RCD(K,N)$ is maintained when Alexandrov spaces with lower Ricci curvature bounds are doubled or glued together, ensuring stability of curvature properties.

Contribution

It proves the preservation of the $RCD(K,N)$ condition under doubling and gluing in Alexandrov spaces with lower Ricci curvature bounds, extending the understanding of curvature stability.

Findings

$RCD(K,N)$ condition is preserved under doubling.

$RCD(K,N)$ condition is preserved under gluing.

Curvature bounds are stable under these geometric operations.

Abstract

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