Explicit Parametrizations of Willmore Surfaces
Explicit Parametrizations of Willmore Surfaces
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Willmore 曲面的显式参数化
DOI：
10.1063/1.4902274
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发表时间：
2014
影响因子：
2.1
通讯作者：
I. Mladenov
中科院分区：
文献类型：
--
作者：
V. Vassilev;P. Djondjorov;E. Atanassov;M. Hadzhilazova;I. Mladenov
Willmore曲面为所谓的Willmore泛函提供了局部极值，该泛函为每个曲面指定其总的平方平均曲率。有一类特殊的轴对称Willmore曲面，其轮廓曲线满足一个相对简单的常微分方程组。这项工作的目的是给出属于前述族的Willmore曲面的显式参数化为雅可比椭圆函数和椭圆积分。
The Willmore surfaces provide local extrema to the so-called Willmore functional, which assigns to each surface its total squared mean curvature. There is a special class of axially symmetric Willmore surfaces whose profile curves satisfy a relatively simpler system of ordinary differential equations. The aim of this work is to give explicit parametrizations of the Willmore surfaces belonging to the foregoing family in terms of the Jacobian elliptic functions and elliptic integrals.