The metric measure boundary of spaces with Ricci curvature bounded below

Abstract

AbstractWe solve a conjecture raised by Kapovitch, Lytchak and Petrunin in [KLP21] by showing that the metric measure boundary is vanishing on any $${{\,\textrm{RCD}\,}}(K,N)$$ RCD ( K , N ) space $$(X,{\textsf{d}},{\mathscr {H}}^N)$$ ( X , d , H N ) without boundary. Our result, combined with [KLP21], settles an open question about the existence of infinite geodesics on Alexandrov spaces without boundary raised by Perelman and Petrunin in 1996.