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arXiv · 2008.07242

Higher order Wirtinger-type inequalities and sharp bounds for the isoperimetric deficit

Kwok-Kun Kwong·Hojoo Lee
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Abstract

Using Fourier analysis, we derive Wirtinger-type inequalities of arbitrary high order. As applications, we prove various sharp geometric inequalities for closed curves on the Euclidean plane. In particular, we obtain both sharp lower and upper bounds for the isoperimetric deficit.

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Kwok-Kun Kwong, Hojoo Lee. 2020-08-17. Higher order Wirtinger-type inequalities and sharp bounds for the isoperimetric deficit. https://arxiv.org/abs/2008.07242

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