Abstract:In every connected component of every stratum of Abelian differentials, we construct square-tiled surfaces with one vertical and one horizontal cylinder. We show that for all but the hyperelliptic components this can be achieved in the minimum number of squares necessary for a square-tiled surface in that stratum. For the hyperelliptic components, we show that the number of squares required is strictly greater and construct surfaces realising these bounds. Using these surfaces, we demonstrate that pseudo-Anosov homeomorphisms optimising the ratio of Teichmüller to curve graph translation length are, in a reasonable sense, ubiquitous in the connected components of strata of Abelian differentials. Finally, we present a further application to filling pairs on punctured surfaces by constructing filling pairs whose algebraic and geometric intersection numbers are equal.

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中文翻译：

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单圆柱方瓦表面和比率优化伪 Anosovs 的普遍存在

摘要：在每一层阿贝尔微分的每一个连通分量中，我们构造了具有一纵一横圆柱体的方形平铺面。我们表明，对于除超椭圆组件之外的所有组件，这可以在该层中正方形平铺表面所需的最少正方形数量中实现。对于超椭圆分量，我们表明所需的正方形数量要严格得多，并构造实现这些边界的曲面。使用这些曲面，我们证明了优化 Teichmüller 与曲线图平移长度之比的伪 Anosov 同胚，在合理意义上，普遍存在于阿贝尔微分层的连通分量中。最后，

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