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Rigidity of Euclidean Convex Fillings for Ordinary Ambrosio--Kirchheim Mass
Abstract
We prove rigidity for compact integral current fillings with respect to ordinary Ambrosio--Kirchheim mass. Let C⊂Rn be a compact convex body with nonempty interior, n≥1, and let T∈In(X), where X=spt T is compact. Suppose ι:∂ C→ X is an isometric embedding for the Euclidean chord metric and ∂ T=ι#cur∂ C, M(T)=Lebn(C). Then ι extends to a surjective isometry I:C→ X satisfying I#cur C=T. No map from the filling to the convex body is assumed.
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BibTeX
@misc{jiang2026rigidity,
title = {{Rigidity of Euclidean Convex Fillings for Ordinary Ambrosio--Kirchheim Mass}},
author = {Xianfeng Jiang},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.26477},
eprint = {2610.26477},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.26477},
}
RIS
TY - UNPB
TI - Rigidity of Euclidean Convex Fillings for Ordinary Ambrosio--Kirchheim Mass
AU - Xianfeng Jiang
PY - 2026
DA - 2026/10/19
PB - arXiv
DO - 10.48550/arxiv.2610.26477
UR - https://arxiv.org/abs/2610.26477
AB - We prove rigidity for compact integral current fillings with respect to ordinary Ambrosio--Kirchheim mass. Let C⊂R^n be a compact convex body with nonempty interior, n≥1, and let T∈I_n(X), where X=spt T is compact. Suppose ι:∂ C→ X is an isometric embedding for the Euclidean chord metric and ∂ T=ι_#cur∂ C, M(T)=Leb^n(C). Then ι extends to a surjective isometry I:C→ X satisfying I_#cur C=T. No map from the filling to the convex body is assumed.
ER -