Filling minimality and Lipschitz-volume rigidity of convex bodies among integral current spaces
Abstract
In this paper we consider metric fillings of boundaries of convex bodies. We show that convex bodies 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 further applications of this result, we prove a variant of Lipschitz-volume rigidity for round spheres and answer a question of Perales concerning the intrinsic flat convergence of minimizing sequences for the Plateau problem.
Main Authors
Format
Articles
Research article
Published
2023
Series
Subjects
Publication in research information system
Publisher
De Gruyter
The permanent address of the publication
https://urn.fi/URN:NBN:fi:jyu-202402211972Use this for linking
Review status
Peer reviewed
ISSN
0075-4102
DOI
https://doi.org/10.1515/crelle-2023-0076
Language
English
Published in
Journal für die reine und angewandte Mathematik
Citation
- Basso, G., Creutz, P., & Soultanis, E. (2023). Filling minimality and Lipschitz-volume rigidity of convex bodies among integral current spaces. Journal für die reine und angewandte Mathematik, 2023(805), 213-239. https://doi.org/10.1515/crelle-2023-0076
License
Copyright© 2023 De Gruyter