AI 中文总结
研究亏格\(g\geq6\)闭双曲曲面，通过泰希米勒空间相关证明，得出对于特定例外集外双曲度量，长度至多为\(L\)的不同本原闭测地线长度数量有下界\(\tau(d)e^{\delta(g)L}\)且\(\delta(g)>\frac{1}{2}\)的结论。
AI 中文摘要
对于每个亏格\(g\geq6\)的闭曲面\(\Sigma_g\)，我们证明存在泰希米勒空间中可数个正余维代数子集的并集，使得对于此例外集之外的每个双曲度量\(d\)，长度至多为\(L\)的不同本原闭测地线长度的数量下界为\(\tau(d)e^{\delta(g)L}\)，其中显式常数\(\delta(g)>\frac{1}{2}\)。
英文摘要
For every closed surface $Σ_g$ of genus $g\geq6$, 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 $δ(g)>\frac12$.
