Calculus of Variations and Geometric Measure Theory

E. Bruè - A. Mondino - D. Semola

The metric measure boundary of spaces with Ricci curvature bounded below

created by mondino on 24 May 2022
modified by semola on 17 May 2024


Published Paper

Inserted: 24 may 2022
Last Updated: 17 may 2024

Journal: Geom. Funct. Anal.
Volume: 33
Pages: 593--636
Year: 2023

ArXiv: 2205.10609 PDF


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.