Tohoku Mathematical Journal
2015
March
SECOND SERIES VOL. 67, NO. 1

Tohoku Math. J.
67 (2015), 51-82

Title MÖBIUS INVARIANT ENERGIES AND AVERAGE LINKING WITH CIRCLES

Author Jun O'Hara and Gil Solanes

(Received November 22, 2012, revised January 9, 2014)
Abstract. 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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