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.
From: Sebastian Hensel [view email]
[v1]
Mon, 15 Jun 2026 18:09:21 UTC (27 KB)
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