We introduce a Möbius invariant energy associated to planar domains, as well as a generalization to space curves. This generalization is a Möbius version of Banchoff-Pohl's notion of area enclosed by a space curve. A relation with Gauss-Bonnet theorems for complete surfaces in hyperbolic space is also described.
"Möbius invariant energies and average linking with circles." Tohoku Math. J. (2) 67 (1) 51 - 82, 2015. https://doi.org/10.2748/tmj/1429549579