论文标题
分布非负性固有曲率的弱规则表面的凸度
Convexity of weakly regular surfaces of distributional nonnegative intrinsic curvature
论文作者
论文摘要
We prove that the image of an isometric embedding into ${\mathbb R}^3$ of a two dimensionnal complete Riemannian manifold $(Σ, g)$ without boundary is a convex surface provided both the embedding and the metric $g$ enjoy a $C^{1,α}$ regularity for some $α>2/3$ and the distributional Gaussian curvature of $g$ is nonnegative and非零。该分析必须通过一些有关非常弱的Monge-Ampère方程解决方案的关键观察结果。
We prove that the image of an isometric embedding into ${\mathbb R}^3$ of a two dimensionnal complete Riemannian manifold $(Σ, g)$ without boundary is a convex surface provided both the embedding and the metric $g$ enjoy a $C^{1,α}$ regularity for some $α>2/3$ and the distributional Gaussian curvature of $g$ is nonnegative and nonzero. The analysis must pass through some key observations regarding solutions to the very weak Monge-Ampère equation.
