The metric measure boundary of spaces with Ricci curvature bounded below

We solve a conjecture raised by Kapovitch, Lytchak and Petrunin in [KLP21] by showing that the metric measure boundary is vanishing on any RCD(K, N) space (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.

Automated summary

We solve a conjecture raised by Kapovitch, Lytchak, and Petrunin in [KLP21] by proving that the metric measure boundary vanishes on any RCD(K, N) space (X, d, H-N) without boundary. Our result, in conjunction with [KLP21], settles an open question about the existence of infinite geodesics on Alexandrov spaces without boundary raised by Perelman and Petrunin in 1996.