The metric measure boundary of spaces with Ricci curvature bounded below

Abstract

We solve a conjecture raised by Kapovitch, Lytchak, and Petrunin by showing that the metric measure boundary is vanishing on any $\mathrm{RCD}(K,N)$ space without boundary. Our result, combined with [Kapovitch-Lytchak-Petrunin '21], settles an open question about the existence of infinite geodesics on Alexandrov spaces without boundary raised by Perelman and Petrunin in 1996.

Cited by in corpus (2)

• Symmetrized and non-symmetrized Asymptotic Mean Value Laplacian in metric measure spaces
• On manifolds with almost non-negative Ricci curvature and integrally-positive $k^{th}$-scalar curvature