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arXiv · 2512.15329

Weak curvature conditions on metric graphs

Juliane Krautz
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Abstract

Starting from pointwise gradient estimates for the heat semigroup, we study three characterizations of weak lower curvature bounds on metric graphs. More precisely, we prove the equivalence between a weak notion of the Bakry-\'Emery curvature condition, a weak Evolutionary Variational Inequality and a weak form of geodesic convexity. The proof is based on a careful regularization of absolutely continuous curves together with an explicit representation of the Cheeger energy. We conclude with a brief discussion on possible applications to the Schr\"odinger bridge problem on metric graphs.

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Juliane Krautz. 2025-12-17. Weak curvature conditions on metric graphs. https://arxiv.org/abs/2512.15329

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