Tarik Aougab

activity

20082026

most citedMinimally intersecting filling pairs on surfaces

31 citations · 100 across the 28 of their papers we have counts for

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Showing 2013Show all

4 papers · 1 filter

math.GT2013★ 31 cited

Minimally intersecting filling pairs on surfaces

Tarik Aougab, Shinnyih Huang

Let $S_{g}$ denote the closed orientable surface of genus $g$ . We construct exponentially many mapping class group orbits of pairs of simple closed curves which fill $S_{g}$ and in…

math.DG2013★ 4 cited

On curves and polygons with the equiangular chord property

Tarik Aougab, Xidian Sun, Serge Tabachnikov +1

Let $C$ be a smooth, convex curve on either the sphere $S^{2}$ , the hyperbolic plane $H^{2}$ or the Euclidean plane $E^{2}$ , with the following property:…

math.GT2013★ 11 cited

Small intersection numbers in the curve graph

Tarik Aougab, Samuel J. Taylor

Let $S_{g, p}$ denote the genus $g$ orientable surface with $p \geq 0$ punctures, and let $ω (g, p) = 3 g + p - 4$ . We prove the existence of infinitely long geodesic rays $\left\{v_{0},v_{1…

math.GT2013★ 1 cited

Quadratic Bounds on the Quasiconvexity of Nested Train Track Sequences

Tarik Aougab

Let $S_{g, p}$ denote the genus $g$ orientable surface with $p$ punctures. We show that nested train track sequences constitute $O ((g, p)^{2})$ -quasiconvex subsets of the curve graph…