中心仿射超曲面的一类变分问题(英文)

On some variational problem for centroaffine hypersurfaces

作者研究了中心仿射超曲面的一类保持体积不变的变分问题以及它的Euler-La-grange方程,这是一个非线性的四阶PDE,通过研究边界问题可以构造很多欧氏完备的解。

Some variation preserving the volume are studied for centroaffine hypersurfaces and its Euler- Lagrange equation, which is a fourth order nonlinear PDE. By solving some boundary problem of a fourth order PDE, we can construct many Euclidean complete centroaffine hypersurfaces satisfying the PDE.