A strong form of the Quantitative Isoperimetric inequality

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.

References in corpus (2)

• Minimality via second variation for a nonlocal isoperimetric problem
• Isoperimetric problem with a Coulombic repulsive term

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• Quantitative isoperimetric inequalities for classical capillarity problems
• Quantitative lower bounds to the Euclidean and the Gaussian Cheeger constants
• Uniqueness results for critical points of a non-local isoperimetric problem via curve shortening
• Remark on a nonlocal isoperimetric problem