Weak curvature conditions on metric graphs
Fuente:
arXiv
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| Autor principal: | |
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| Formato: | Preprint |
| Publicado: |
2025
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| Materias: | |
| Acceso en línea: | |
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| _version_ | 1866908718091730944 |
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| author | Krautz, Juliane |
| author_facet | Krautz, Juliane |
| contents | 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-Émery 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 Schrödinger bridge problem on metric graphs. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_15329 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Weak curvature conditions on metric graphs Krautz, Juliane Analysis of PDEs 35R02, 47D07, 60B05 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-Émery 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 Schrödinger bridge problem on metric graphs. |
| title | Weak curvature conditions on metric graphs |
| topic | Analysis of PDEs 35R02, 47D07, 60B05 |
| url | https://arxiv.org/abs/2512.15329 |