Characterizations of Forman curvature

Jürgen Jost; Florentin Münch

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arXiv · 2110.04554

Characterizations of Forman curvature

Jürgen Jost·Florentin Münch

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Abstract

We characterize Forman curvature lower bounds via contractivity of the Hodge Laplacian semigroup. We prove that Ollivier and Forman curvature coincide on edges when maximizing the Forman curvature over the choice of 2-cells. To this end, we translate between 2-cells and transport plans. Moreover, we give improved diameter bounds. We explicitly warn the reader that our Forman curvature notion does not coincide with Forman's original definition, but can be seen as generalization of the latter one.

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BibTeX RIS

Jürgen Jost, Florentin Münch. 2021-10-09. Characterizations of Forman curvature. https://arxiv.org/abs/2110.04554

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