A1 Journal article (refereed)
Filling minimality and Lipschitz-volume rigidity of convex bodies among integral current spaces (2023)

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

JYU authors or editors

Publication details

All authors or editors: Basso, Giuliano; Creutz, Paul; Soultanis, Elefterios

Journal or series: Journal für die reine und angewandte Mathematik

ISSN: 0075-4102

eISSN: 1435-5345

Publication year: 2023

Publication date: 01/11/2023

Volume: 2023

Issue number: 805

Pages range: 213-239

Publisher: De Gruyter

Publication country: Germany

Publication language: English

DOI: https://doi.org/10.1515/crelle-2023-0076

Publication open access: Not open

Publication channel open access: 

Publication is parallel published (JYX): https://jyx.jyu.fi/handle/123456789/93505

Web address of parallel published publication (pre-print): https://arxiv.org/abs/2209.12545

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.

Keywords: differential geometry

Contributing organizations

Ministry reporting: Yes

VIRTA submission year: 2023

JUFO rating: 3