M��bius invariant energies and average linking with circles

We define and study a M��bius invariant energy associated to planar domains, as well its generalization to space curves. This generalization is a M��bius 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.
36 pages Minor changes in version 2