论文标题
填充最小的和Lipschitz-volume-volume刚性的刚性刚度
Filling minimality and Lipschitz-volume rigidity of convex bodies among integral current spaces
论文作者
论文摘要
在本文中，我们考虑了凸体的度量填充物。我们证明凸体$ c \ subset \ mathbb {r}^n $是所有积分电流空间中其边界指标的独特填充物。为此，我们还证明了凸体在积分电流空间的类别中享受Lipschitz-volume刚性属性，这在平滑类别中是众所周知的。作为此结果的进一步应用，我们回答了一个有关高原问题最小化序列的固有平面收敛性的问题。
In this paper we consider metric fillings of convex bodies. We show that convex bodies $C\subset \mathbb{R}^n$ are the unique minimal fillings of their boundary metrics among all integral current spaces. To this end, we also prove that convex bodies enjoy the Lipschitz-volume rigidity property within the category of integral current spaces, which is well known in the smooth category. As a further application of this result, we answer a question of Perales concerning the intrinsic flat convergence of minimizing sequences for the Plateau problem.
