Filling minimality and Lipschitz-volume rigidity of convex bodies among integral current spaces
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2022
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| _version_ | 1866909180642721792 |
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| author | Basso, Giuliano Creutz, Paul Soultanis, Elefterios |
| author_facet | Basso, Giuliano Creutz, Paul Soultanis, Elefterios |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2209_12545 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Filling minimality and Lipschitz-volume rigidity of convex bodies among integral current spaces Basso, Giuliano Creutz, Paul Soultanis, Elefterios Differential Geometry Functional Analysis Metric Geometry 53C23, 49Q15 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. |
| title | Filling minimality and Lipschitz-volume rigidity of convex bodies among integral current spaces |
| topic | Differential Geometry Functional Analysis Metric Geometry 53C23, 49Q15 |
| url | https://arxiv.org/abs/2209.12545 |