The metric space of geodesic laminations on a surface: I

Abstract

We consider the space of geodesic laminations on a surface, endowed with the Hausdorff metric d_H and with a variation of this metric called the d_log metric. We compute and/or estimate the Hausdorff dimensions of these two metrics. We also relate these two metrics to another metric which is combinatorially defined in terms of train tracks.

Published by Geometry and Topology at http://www.maths.warwick.ac.uk/gt/GTVol8/paper13.abs.html

References in corpus (2)

• Geometry of the Complex of Curves I: Hyperbolicity
• The metric space of geodesic laminations on a surface II: small surfaces

Cited by in corpus (3)

• On the topology of ending lamination space
• Shear-shape cocycles for measured laminations and ergodic theory of the earthquake flow
• Continuity of the orthogeodesic foliation and ergodic theory of the earthquake flow