We show that the sectional capacity of an adelic subset of a projective variety over a number field is a quasi-canonical limit of arithmetic top self-intersection numbers, and we establish the functorial properties of extremal plurisubharmonic Green's functions. We also present a conjecture that the sectional capacity should be a top selfintersection number in an appropriate adelic arithmetic intersection theory.
Ted Chinburg. Chi Fong Lau. Robert Rumely. "Capacity theory and arithmetic intersection theory." Duke Math. J. 117 (2) 229 - 285, 1 April 2003. https://doi.org/10.1215/S0012-7094-03-11722-6