A note on the uniqueness of minimal length carrier graphs
arXiv:1208.2241
Abstract
We show that minimal length carrier graphs are not unique, but if M is in a large class of hyperbolic 3-manifolds, including the geometrically finite ones, then M has only finitely many minimal length carrier graphs and no two of them are homotopic. As a corollary, we obtain a new proof that the isometry group of a geometrically finite 3-manifold is finite.
10 pages, 1 figure; Added an application and fixed small error