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Tohoku Mathematical Journal
SECOND SERIES VOL. 67, NO. 1
|Tohoku Math. J.|
67 (2015), 51-82
MÖBIUS INVARIANT ENERGIES AND AVERAGE LINKING WITH CIRCLES
Jun O'Hara and Gil Solanes
(Received November 22, 2012, revised January 9, 2014)
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.
Mathematics Subject Classification.
Primary 53A30; Secondary 53C65.
Key words and phrases.
Möbius geometry, integral geometry, knot energies, renormalization, symplectic form.
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