Calculus of Variations and Geometric Measure Theory

V. Kapovitch - A. Mondino

On the topology and the boundary of $N$-dimensional $RCD(K,N)$ spaces

created by mondino on 08 Jul 2019
modified on 31 Mar 2020


Accepted Paper

Inserted: 8 jul 2019
Last Updated: 31 mar 2020

Journal: Geometry & Topology
Year: 2019


We establish topological regularity and stability of N-dimensional RCD(K,N) spaces (up to a small singular set), also called non-collapsed RCD(K,N) in the literature. We also introduce the notion of a boundary of such spaces and study its properties, including its behavior under Gromov-Hausdorff convergence.