Published Paper

Inserted: 24 may 2022
Last Updated: 17 may 2024

Journal: Geom. Funct. Anal.
Volume: 33
Pages: 593--636
Year: 2023
Doi: https://doi.org/10.1007/s00039-023-00626-x

Abstract:

We solve a conjecture raised by Kapovitch, Lytchak and Petrunin 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 previous work by Kapovitch-Lytchak-Petrunin, settles an open question about the existence of infinite geodesics on Alexandrov spaces without boundary raised by Perelman and Petrunin in 1996.