Möbius invariant energies and average linking with circles

Abstract

We define and study a Möbius invariant energy associated to planar domains, as well its 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.

36 pages Minor changes in version 2

References in corpus (1)

• Renormalization of potentials and generalized centers

Cited by in corpus (2)

• Renormalization of potentials and generalized centers
• Möbius Invariants of Shapes and Images