第十章、极小曲面

Differential Geometry之第十章极小曲面-LMLPHP

1.极小图

Differential Geometry之第十章极小曲面-LMLPHP

Differential Geometry之第十章极小曲面-LMLPHP

Differential Geometry之第十章极小曲面-LMLPHP

Differential Geometry之第十章极小曲面-LMLPHP

Differential Geometry之第十章极小曲面-LMLPHP

Animation showing the deformation of a helicoid into a catenoid.

Differential Geometry之第十章极小曲面-LMLPHP

Differential Geometry之第十章极小曲面-LMLPHP

Differential Geometry之第十章极小曲面-LMLPHP

Differential Geometry之第十章极小曲面-LMLPHP

Differential Geometry之第十章极小曲面-LMLPHP

Animation of Scherk's first and second surface transforming into each other: they are members of the same associate family of minimal surfaces.

1.1.极小图的等温坐标

Differential Geometry之第十章极小曲面-LMLPHP

Differential Geometry之第十章极小曲面-LMLPHP

1.2.Bernstein定理

Differential Geometry之第十章极小曲面-LMLPHP

Differential Geometry之第十章极小曲面-LMLPHP

2.极小曲面的Weierstrass表示

Differential Geometry之第十章极小曲面-LMLPHP

Differential Geometry之第十章极小曲面-LMLPHP

Differential Geometry之第十章极小曲面-LMLPHP

Differential Geometry之第十章极小曲面-LMLPHP

Differential Geometry之第十章极小曲面-LMLPHPDifferential Geometry之第十章极小曲面-LMLPHP

Enneper surface ,Differential Geometry之第十章极小曲面-LMLPHP

Differential Geometry之第十章极小曲面-LMLPHP

Costa曲面,亏格为1的完备极小嵌入曲面。

Differential Geometry之第十章极小曲面-LMLPHP

3.极小曲面的Gauss映射

亚纯函数是在区域D上有定义,且除去极点之外处处解析的函数。

Differential Geometry之第十章极小曲面-LMLPHP

Differential Geometry之第十章极小曲面-LMLPHP

Differential Geometry之第十章极小曲面-LMLPHP

Differential Geometry之第十章极小曲面-LMLPHP

Differential Geometry之第十章极小曲面-LMLPHP

Differential Geometry之第十章极小曲面-LMLPHP

Differential Geometry之第十章极小曲面-LMLPHP

Differential Geometry之第十章极小曲面-LMLPHP

4.面积的变分与稳定极小曲面

Differential Geometry之第十章极小曲面-LMLPHP

Differential Geometry之第十章极小曲面-LMLPHP

Differential Geometry之第十章极小曲面-LMLPHP

05-11 18:38