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June 2010 Laguerre Arc Length from Distance Functions
David E. Barrett, Michael Bolt
Asian J. Math. 14(2): 213-234 (June 2010).


For the Laguerre geometry in the dual plane, invariant arc length is shown to arise naturally through the use of a pair of distance functions. These distances are useful for identifying equivalence classes of curves, within which the extremal curves are proved to be strict maximizers of Laguerre arc length among three-times differentiable curves of constant signature in a prescribed isotopy class. For smoother curves, it is shown that Laguerre curvature determines the distortion of the distance functions. These results extend existing work for the Möbius geometry in the complex plane.


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David E. Barrett. Michael Bolt. "Laguerre Arc Length from Distance Functions." Asian J. Math. 14 (2) 213 - 234, June 2010.


Published: June 2010
First available in Project Euclid: 11 January 2011

zbMATH: 1225.51002
MathSciNet: MR2746121

Primary: 51B15
Secondary: 53A35 , 58E35

Keywords: Distance function , dual number , Laguerre arc length , Laguerre geometry

Rights: Copyright © 2010 International Press of Boston

Vol.14 • No. 2 • June 2010
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