Higher order Wirtinger-type inequalities and sharp bounds for the isoperimetric deficit
Differential Geometry
2020-08-18 v1 Functional Analysis
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.
Keywords
Cite
@article{arxiv.2008.07242,
title = {Higher order Wirtinger-type inequalities and sharp bounds for the isoperimetric deficit},
author = {Kwok-Kun Kwong and Hojoo Lee},
journal= {arXiv preprint arXiv:2008.07242},
year = {2020}
}
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