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

Authors

Kwok Kun Kwong, University of Wollongong
Hojoo Lee, Jeonbuk National University

Publication Name

Proceedings of the American Mathematical Society

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.

Open Access Status

This publication may be available as open access

Volume

149

Issue

11

First Page

4825

Last Page

4840