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arXiv · 2606.17172

The quantitative isoperimetric inequality: A calibration argument

Sebastian Hensel·Tim Laux
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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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Sebastian Hensel, Tim Laux. 2026-06-15. The quantitative isoperimetric inequality: A calibration argument. https://arxiv.org/abs/2606.17172

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