论文标题
矫正孔，凹入核心和双曲线表面的身份家族
Prime orthogeodesics, concave cores and families of identities on hyperbolic surfaces
论文作者
论文摘要
我们证明并探索了一系列身份，这些家族与双曲线表面的曲线和矫正曲线相关。这些身份在大量的指标上存在，包括具有双曲线点的指标，尤其是显示了如何将第一作者的结果扩展到带有牙齿的表面。该方法中的主要成分之一是根据其动力学行为的一组矫形地理学分配到集合中，可以通过将它们与Orbifold表面上的大地学联系起来，可以通过几何理解。这些轨道表面恰好在基础身份所拥有的空间的边界上。
We prove and explore a family of identities relating lengths of curves and orthogeodesics of hyperbolic surfaces. These identities hold over a large space of metrics including ones with hyperbolic cone points, and in particular, show how to extend a result of the first author to surfaces with cusps. One of the main ingredients in the approach is a partition of the set of orthogeodesics into sets depending on their dynamical behavior, which can be understood geometrically by relating them to geodesics on orbifold surfaces. These orbifold surfaces turn out to be exactly on the boundary of the space in which the underlying identity holds.
