凸体在积分电流空间中的填充极小性与 Lipschitz-体积刚性
微分几何
2024-04-26 v3 泛函分析
度量几何
摘要
本文考虑凸体的度量填充。我们证明凸体 是所有积分电流空间中其边界度量的唯一极小填充。为此，我们还证明了凸体在积分电流空间范畴内具有 Lipschitz-体积刚性性质，该性质在光滑范畴中是众所周知的。作为该结果的进一步应用，我们回答了 Perales 关于 Plateau 问题极小序列的内蕴平坦收敛的一个问题。
引用
@article{arxiv.2209.12545,
title = {Filling minimality and Lipschitz-volume rigidity of convex bodies among integral current spaces},
author = {Giuliano Basso and Paul Creutz and Elefterios Soultanis},
journal= {arXiv preprint arXiv:2209.12545},
year = {2024}
}
备注
25 pages, 1 figure, v3: we have added Corollary 1.3 concerning the LV-rigidity of the sphere. In version 2 we had already added Theorem 1.1, a filling minimality result for convex bodies