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

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.

Cited by in corpus (3)

• Explicit formulas for heat kernels on diamond fractals
• Canonical diffusions on the pattern spaces of aperiodic Delone sets
• Dual graphs and modified Barlow--Bass resistance estimates for repeated barycentric subdivisions