On the topology and the boundary ofN–dimensional RCD(K,N) spaces
Vitali Kapovitch, Andrea Mondino
Abstract
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.
Topics & Concepts
MathematicsBoundary (topology)Hausdorff spaceTopology (electrical circuits)Pure mathematicsConvergence (economics)Set (abstract data type)Topological spaceStability (learning theory)Mathematical analysisCombinatoricsComputer scienceEconomicsMachine learningProgramming languageEconomic growthGeometric Analysis and Curvature FlowsGeometry and complex manifoldsPoint processes and geometric inequalities