Minimal stretch maps between hyperbolic surfaces
Abstract
This paper develops a theory of Lipschitz comparisons of hyperbolic surfaces analogous to the theory of quasiconformal comparisons. Extremal Lipschitz maps (minimal stretch maps) and geodesics for the `Lipschitz metric' are constructed. The extremal Lipschitz constant equals the maximum ratio of lengths of measured laminations, which is attained with probability one on a simple closed curve. Cataclysms are introduced, generalizing earthquakes by permitting more violent shearing in both directions along a fault. Cataclysms provide useful coordinates for Teichmuller space that are convenient for computing derivatives of geometric function in Teichmuller space and measured lamination space.
 Publication:

arXiv Mathematics eprints
 Pub Date:
 January 1998
 arXiv:
 arXiv:math/9801039
 Bibcode:
 1998math......1039T
 Keywords:

 Geometric Topology;
 Differential Geometry;
 57m50
 EPrint:
 53 pages, 11 figures, version of 1986 preprint