论文标题
长度最小化水平曲线通过校准
Length-minimizing level curves via calibrations
论文作者
论文摘要
我们提出了一个基本标准，用于显示大量共形度量的大量测量学特性的长度最小化特性。特别是，我们证明了谐波函数的级别曲线的长度最小化属性，以及在上半部分中带有偏心率$ \ varepsilon $的圆锥形段家族的长度最小化属性，并带有结构化度量$ \ weft（{\ varepsilon}^{2} + \ frac {1} \;} \ right）\ left（dx^{2} + dy^{2} \ right）$。
We present an elementary criterion to show the length-minimizing property of geodesics for a large class of conformal metrics. In particular, we prove the length-minimizing property of level curves of harmonic functions and the length-minimizing property of a family of the conic sections with the eccentricity $\varepsilon$ in the upper half plane endowed with the conformal metric $ \left( {\varepsilon}^{2} + \frac{1}{\;{y^2} \;} \right) \left(dx^{2} + dy^{2} \right)$.
