A note on the uniqueness of minimal length carrier graphs

Michael Siler

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arXiv · 1208.2241

A note on the uniqueness of minimal length carrier graphs

Michael Siler

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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.

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Michael Siler. 2012-08-10. A note on the uniqueness of minimal length carrier graphs. https://arxiv.org/abs/1208.2241

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