On the length sets of closed hyperbolic surfaces

2026/07/23 by Yanlong Hao
#math.GT

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Abstract

For every closed surface Σ_g of genus g≥6, we prove that there exists a countable union of positive-codimension algebraic subsets of Teichmüller space such that, for every hyperbolic metric d outside this exceptional set, the number of distinct primitive closed-geodesic lengths at most L is bounded below by τ(d)e^δ(g)L, where the explicit constant δ(g) satisfies δ(g)>\frac12.

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