A short proof of the bounded geodesic image theorem

Abstract

We give a combinatorial proof, using the hyperbolicity of the curve graphs, of the bounded geodesic image theorem of Masur and Minsky. Recently it has been shown that curve graphs are uniformly hyperbolic, thus a universal bound can be given for the diameter of the geodesic image. We also generalize the theorem for projections to markings of the whole surface.

7 pages, 3 figures

References in corpus (2)

• Slim unicorns and uniform hyperbolicity for arc graphs and curve graphs
• Uniform Hyperbolicity of the Graphs of Curves

Cited by in corpus (5)

• Boundaries and automorphisms of hierarchically hyperbolic spaces
• Small intersection numbers in the curve graph
• Uniform local finiteness of the curve graph via subsurface projections
• Efficient geodesics and an effective algorithm for distance in the complex of curves
• Intersection numbers in the curve complex via subsurface projections