An inequality for the minimum affine curvature of a plane curve
type: Item
instance of: scholarly article
title: An inequality for the minimum affine curvature of a plane curve
zbMATH Open document ID: 1445.51010
author: Yunlong Yang
published in: Comptes Rendus. Mathématique. Académie des Sciences, Paris
publication date: 2020-08-03T00:00:00Z
review text: In the paper the following inequality for the minimum affine curvature \(\mu_\text{min}\) of a planar smooth simple closed curve \(\gamma\) is given: \[\mu_\text{min}\leq(\pi/A)^{2/3},\] where \(A\) is the enclosed area of \(\gamma\). The inequality is obtained as an application of the affine curve shortening flow and the affine isoperimetric inequality \[\mathcal L^3\leq 8\pi^2A\] for a closed convex curve \(\gamma\), where \(\mathcal L\) and \(A\) are the affine length and the enclosed area of \(\gamma\), respectively.
reviewed by: Martin Lukarevski
Mathematics Subject Classification ID: 51M16
Mathematics Subject Classification ID: 52A40
Mathematics Subject Classification ID: 53A04
zbMATH DE Number: 7226769
zbMATH Keywords: affine curvature
zbMATH Keywords: affine curve shortening flow
zbMATH Keywords: affine isoperimetric inequality
MaRDI profile type: Publication
full work available at URL: crmath.19
OpenAlex ID: W3034687466
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DOI: 10.5802/CRMATH.19
description: scientific article; zbMATH DE number 7226769