Open Access
2015 Möbius invariant energies and average linking with circles
Jun O'Hara, Gil Solanes
Tohoku Math. J. (2) 67(1): 51-82 (2015). DOI: 10.2748/tmj/1429549579


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.


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Jun O'Hara. Gil Solanes. "Möbius invariant energies and average linking with circles." Tohoku Math. J. (2) 67 (1) 51 - 82, 2015.


Published: 2015
First available in Project Euclid: 20 April 2015

zbMATH: 06441343
MathSciNet: MR3337963
Digital Object Identifier: 10.2748/tmj/1429549579

Primary: 53A30
Secondary: 53C65

Keywords: integral geometry , knot energies , Möbius geometry , renormalization , symplectic form

Rights: Copyright © 2015 Tohoku University

Vol.67 • No. 1 • 2015
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