Remarks on the continuity of convex functions in geodesic spaces - López-Acedo, Genaro; Nicolae, Adriana (Topological Methods in Nonlinear Analysis, 2024)
We explore the behavior of convex functions defined on locally polyhedral type spaces. As a relevant example of such spaces we show that locally compact$\mathbb{R}$-trees with the geodesic extension property around any point are locally polyhedral spaces.