Quasiconvexity in the curve complex

By H. Masur, Yair N. Minsky. 2003

73 citations recorded by the source corpus.

Let S be the boundary of a handlebody M. We prove that the set of curves in S that are boundaries of disks in M, considered as a subset of the complex of curves of S, is quasi-convex.

Subfields: Applied Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/df3055ef6a91e195cb7eff6a8270a3323f853843

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In Applied Mathematics

In Geometry and Topology

Citations in the corpus

The geometry of the disk complex (2010, background): “en the map n7!ˇ Y(˝ n), as parameterized by splittings, is an A{unparameterized quasi-geodesic. Note that, when Y = S, Theorem 18.2 is essentially due to the rst author and Minsky; see Theorem 1.3 of [26]. In Section 5.2 of [27], for every sliding and splitting sequence f˝ ngN n=0 and for any essent”
Geometry of the complex of curves and of Teichmüller space (2005, methodology): “rm quasi-geodesics. It turns out that up to parametrization, these curves are indeed p-quasi-geodesics in C(S) for a universal number p > 0 only depending on the topological type of the surface S ([20], see also [7]). To explain this fact we use the following construction of Bowditch [2]. For mul”
Random Heegaard splittings (2008, methodology): “Masur and Minsky [15] have shown that the resulting relative space is quasiisometric to the complex of curves.”
Uniform hyperbolicity of the graphs of curves (2012, unknown): “We note that this constant B also occurs in the proof of the quasiconvexity of the disk set by Masur and Minsky in [14].”
Random walks on the mapping class group (2006, background): “adapt a result of Kerckhoﬀ [13] to show that the harmonic measure of the disc set is zero, so generically the stable and unstable laminations do not lie in the disc set. Furthermore, Masur and Minsky [18] have shown that the disc set is quasiconvex, so if the translation length of a pseudo-Anosov el”
Spaces of Kleinian Groups: Train tracks and the Gromov boundary of the complex of curves (2004, background): “Klarreich’s proof of the above theorem relies on Teichmüller theory and the results of Masur and Minsky in [MM1].”
Train tracks and the geometry of the complex of curves (2005, background): “It turns our that up to parametrization, these curves are indeed q-quasi-geodesics in C(S) for a universal number q > 0 only depending on the topological type of the surface S ([16], see also [8]).”