A strong form of the Quantitative Isoperimetric inequality
Nicola Fusco, Vesa Julin
TL;DR
This paper refines the quantitative isoperimetric inequality by showing that the isoperimetric gap influences both the Fraenkel asymmetry and boundary oscillation, providing a deeper understanding of shape optimization.
Contribution
It introduces a stronger form of the inequality linking the isoperimetric gap to boundary oscillation and asymmetry, advancing the theoretical framework.
Findings
The isoperimetric gap controls boundary oscillation.
The inequality refinement links asymmetry and boundary behavior.
Provides new bounds for shape deviations.
Abstract
We give a refinement of the quantitative isoperimetric inequality. We prove that the isoperimetric gap controls not only the Fraenkel asymmetry but also the oscillation of the boundary.
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