论文标题
大规模保护的刚度$ 1 $ -LIPSCHITZ地图从积分电流空间到$ \ Mathbb {r}^n $
Rigidity of mass-preserving $1$-Lipschitz maps from integral current spaces into $\mathbb{R}^n$
论文作者
论文摘要
我们证明，从这个空间到$ n $维的欧几里得球，鉴于$ n $维的当前空间和$ 1 $ -Lipschitz的地图，它保留了电流的质量并在边界上具有注射量，然后地图必须是一个等值线。因此，我们推断出相对于固有的平坦距离的稳定性结果，这意味着最初由Huang-Lee-Sormani提出的图形歧管的正质量定理的稳定性。
We prove that given an $n$-dimensional integral current space and a $1$-Lipschitz map, from this space onto the $n$-dimensional Euclidean ball, that preserves the mass of the current and is injective on the boundary, then the map has to be an isometry. We deduce as a consequence a stability result with respect to the intrinsic flat distance, which implies the stability of the positive mass theorem for graphical manifolds as originally formulated by Huang--Lee--Sormani.
