论文标题
$ c^{1，α} $的几何形状
The geometry of $C^{1,α}$ flat isometric immersions
论文作者
论文摘要
我们表明，如果它喜欢LittleHöldergemulairty $ c^{1,2/3} $，则可以开发将平面域的任何等距沉浸在$ \ Mathbb r^3 $中。尤其是，与$α> 2/3 $的局部$ c^{1，α} $的等距浸入属于此类。该证明是基于这种沉浸式的第二基本形式的弱概念，在这种弱环境中对高斯 - 科达兹 - 梅纳尔迪方程的分析，以及对莱维卡分析的堕落蒙加利亚方程非常弱的解决方案的相似解决方案和第二作者。
We show that any isometric immersion of a flat plane domain into $\mathbb R^3$ is developable provided it enjoys the little Hölder regulairty $c^{1,2/3}$. In particular, isometric immersions of local $C^{1,α}$ regularity with $α> 2/3$ belong to this class. The proof is based on the existence of a weak notion of second fundamental form for such immersions, the analysis of the Gauss-Codazzi-Mainardi equations in this weak setting, and a parallel result on the very weak solutions to the degenerate Monge-Ampère equation analyzed by Lewicka and the second author.
