Document Type

Article

Publication Title

Asian Journal of Mathematics

Abstract

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. © 2010 International Press.

First Page

213

Last Page

234

DOI

10.4310/AJM.2010.v14.n2.a3

Publication Date

1-1-2010

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