Mathematics

In this talk, we show the stability of the curvature-dimension condition for negative values of the generalized dimension parameter under a suitable notion of convergence. We start by presenting an appropriate setting to introduce the CD(K, N)-condition for N < 0, allowing metric measure structures in which the reference measure is quasi-Radon. Then in this class of spaces we introduce the distance $d_{\mathsf{iKRW}}$, which extends the already existing  notions of distance between metric measure spaces. Finally, we prove that if a sequence of metric measure spaces satisfying the CD(K, N)-condition with N < 0 is converging with respect to the distance $d_{\mathsf{iKRW}}$ to some metric measure space, then this limit structure is still a CD(K, N) space.