论文标题
长度最小值，用于无限的填充封闭曲线的家族
Length minima for an infinite family of filling closed curves on a one-holed torus
论文作者
论文摘要
We explicitly find the minima as well as the minimum points of the geodesic length functions for the family of filling (hence non-simple) closed curves, $a^2b^n$ ($n\ge 3$), on a complete one-holed hyperbolic torus in its relative Teichmüller space, where $a, b$ are simple closed curves on the one-holed torus which intersect exactly once transversely.这为问题提供了具体的示例，以最大程度地减少其相对Teichmüller空间中有限型的固定封闭曲线的固定填充闭合曲线的地球长度。
We explicitly find the minima as well as the minimum points of the geodesic length functions for the family of filling (hence non-simple) closed curves, $a^2b^n$ ($n\ge 3$), on a complete one-holed hyperbolic torus in its relative Teichmüller space, where $a, b$ are simple closed curves on the one-holed torus which intersect exactly once transversely. This provides concrete examples for the problem to minimize the geodesic length of a fixed filling closed curve on a complete hyperbolic surface of finite type in its relative Teichmüller space.
