On the continuity of geodesically convex functions on Riemannian manifolds
Authors
Victor-Emmanuel Brunel
Pierre Pansu
Abstract
In this short note, we prove that all geodesically convex functions defined on a Riemannian manifold are continuous in the interior of their domain. This is a folklore result, but to the best of our knowledge, there is only one available proof, which is largely cited. However, it contains a significant gap, which we fill here. We also discuss extensions of this result beyond the Riemannian setting.
