极小曲面的凸水平集的曲率关于函数高度的凸性（英文）

The Convexity of the Curvature of the Convex Level Sets of Minimal Surface with Respect to the Height

对于R2中水平集严格凸的极小曲面,通过一个辅助函数研究水平集的曲率,可以得到曲率函数关于极小曲面函数高度的凸性,并且可以标明我们的结果是最佳的,

For the minimal graph with strictly convex level sets in R2, we take an auxiliary function to study the curvature of the level sets. We obtain the convexity of the curvature function with respect to the height of the minimal surface. We also show that our result is optimal.