Differential one-forms on Dirichlet spaces and Bakry-Émery estimates on metric graphs

Baudoin, Fabrice; Kelleher, Daniel

doi:10.1090/tran/7362

Differential one-forms on Dirichlet spaces and Bakry-Émery estimates on metric graphs
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by Fabrice Baudoin and Daniel J. Kelleher PDF

Trans. Amer. Math. Soc. 371 (2019), 3145-3178 Request permission

Abstract:

We develop a general framework on Dirichlet spaces to prove a weak form of the Bakry-Émery estimate and study its consequences. This estimate may be satisfied in situations, like metric graphs, where generalized notions of Ricci curvature lower bounds are not available.

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