平面打结闭曲线上扁形椭圆环面的全平均曲率——Willmore猜想的一个推广

The Completely Equally Curvature of Ellipse Torus on the Planes Closed Curve

给出了Willmore猜想的一个推广,说明平面打结闭曲线上扁形椭圆环面的全平均曲率蓦∫M2H2dA≥4π2p2,其中p为椭圆的短轴与长轴之比。

This paper affords a special case about T.J.Willmore＇s supposition.The completely equally curvature of Ellipse torus on the plane closed curve that supports ∫M2H2dA≥4π2p2,p is the ratio of short axis and long axis of the Ellipse.