Centroaffine Bernstein problems
Centroaffine Bernstein problems
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DOI：
10.1016/j.difgeo.2003.12.004
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发表时间：
2004-05
影响因子：
0.5
通讯作者：
An-Min Li;Haizhong Li;U. Simon
中科院分区：
文献类型：
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作者：
An-Min Li;Haizhong Li;U. Simon
王cp [Geom]。Dedicata 51(1994) 63-74]研究了超曲面的中心仿射面积泛函的欧拉-拉格朗日方程。就超曲面作为图的局部表示而言，该方程是一个复杂的、强非线性的四阶偏微分方程。我们考虑满足这些方程的解和完备性条件。我们还提出了合适的中仿射Bernstein问题，并给出了部分解。
C.P. Wang [Geom. Dedicata 51 (1994) 63–74] studied the Euler–Lagrange equation for the centroaffine area functional of hypersurfaces. In terms of a local representation of the hypersurface as a graph, this equation is a complicated, strongly non-linear fourth order PDE. We consider classes of solutions satisfying these equations together with completeness conditions. We also formulate appropriate centroaffine Bernstein problems and give partial solutions.