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

2020/08/17 by Kwok‐Kun Kwong, Kwong, Kwok-Kun, Hojoo Lee +1 · 1 citation
Engineering · Mathematics · #26D10 #28A75 #53A04 #53C42 #Advanced Numerical Analysis Techniques #Differential Geometry (math.DG) #FOS: Mathematics #Functional Analysis (math.FA) #Mechanical Behavior of Composites #Point processes and geometric inequalities

paper · pdf · doi:10.48550/arxiv.2008.07242

openalex publication_date 2020/08/17 · openalex created_date 2022/07/26 · openalex updated_date 2026/07/28

Abstract

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

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• The kth Order Preserving Sets and Isoperimetric Type Inequalities for Planar Ovals

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