Year: 2026
Type: preprint
Abstract: We prove rigidity for compact integral current fillings with respect to ordinary Ambrosio--Kirchheim mass. Let $C\subset\R^n$ be a compact convex body with nonempty interior, $n\ge1$, and let $T\in\I_n(X)$, where $X=\spt T$ is compact. Suppose $ι:\partial C\to X$ is an isometric embedding for the Euclidean chord metric and \[ \partial T=ι_\#\cur{\partial C},\qquad \M(T)=\Leb^n(C). \] Then $ι$ extends to a surjective isometry $I:C\to X$ satisfying $I_\#\cur C=T$. No map from the filling to the convex body is assumed.
Source: arXiv (Cornell University)
Author: Jiang, Xianfeng
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7223061549