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
First Page
213
Last Page
234
DOI
10.4310/AJM.2010.v14.n2.a3
Publication Date
1-1-2010
Recommended Citation
Barrett, David E. and Bolt, Michael, "Laguerre arc length from distance functions" (2010). University Faculty Publications and Creative Works. 358.
https://digitalcommons.calvin.edu/calvin_facultypubs/358