On the continuity of geodesically convex functions on Riemannian manifolds

Fuente: arXiv
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Autori principali: Brunel, Victor-Emmanuel, Pansu, Pierre
Natura: Preprint
Pubblicazione: 2025
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author Brunel, Victor-Emmanuel
Pansu, Pierre
author_facet Brunel, Victor-Emmanuel
Pansu, Pierre
contents 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.
format Preprint
id arxiv_https___arxiv_org_abs_2512_05621
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle On the continuity of geodesically convex functions on Riemannian manifolds
Brunel, Victor-Emmanuel
Pansu, Pierre
Differential Geometry
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.
title On the continuity of geodesically convex functions on Riemannian manifolds
topic Differential Geometry
url https://arxiv.org/abs/2512.05621