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The quantitative isoperimetric inequality: A calibration argument
Abstract
We give a short proof of the quantitative isoperimetric inequality. Our argument is based on a notion of quantitative calibrations which induce a natural distance controlling both the Fraenkel asymmetry and the tilt excess. The proof of our key result which can be viewed as a nonlinear, geometric version of Fuglede's result in BV is direct and self-contained. In particular, we do not make any use of regularity theory for almost minimizers.
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BibTeX
@misc{hensel2026quantitative,
title = {{The quantitative isoperimetric inequality: A calibration argument}},
author = {Sebastian Hensel and Tim Laux},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2606.17172},
eprint = {2606.17172},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2606.17172},
}
RIS
TY - UNPB
TI - The quantitative isoperimetric inequality: A calibration argument
AU - Sebastian Hensel
AU - Tim Laux
PY - 2026
DA - 2026/10/19
PB - arXiv
DO - 10.48550/arxiv.2606.17172
UR - https://arxiv.org/abs/2606.17172
AB - We give a short proof of the quantitative isoperimetric inequality. Our argument is based on a notion of quantitative calibrations which induce a natural distance controlling both the Fraenkel asymmetry and the tilt excess. The proof of our key result which can be viewed as a nonlinear, geometric version of Fuglede's result in BV is direct and self-contained. In particular, we do not make any use of regularity theory for almost minimizers.
ER -