基于极值长度的平坦度量（英文）

The Flat Metric Based On Extremal Length

极值度量是经典共形几何与拟共形几何中重要的研究对象,定义在拓扑四边形上的离散极值度量是平坦度量,由此平坦度量可以构造一种巧妙的组合结构.利用拓扑四边形的离散极值度量,可以实现一种新的共形参数化方法.

Extremal length is a central tool in the literature of conformal and quasiconformal maps. Discrete ex- tremal length defined on topological quadrilateral is a fiat metric, which can be utilized to construct a marvelous combinatorial structure. A novel conformal parameterization method is proposed by use of discrete extremal length defined on topological quadrilateral surfaces.