Some remarks about closed convex curves

Ke Ou, Shengliang Pan

Type: Article

Publication Date: 2010-12-01

Citations: 16

DOI: https://doi.org/10.2140/pjm.2010.248.393

Abstract

We introduce a function w k (θ ) for closed convex plane curves, and then prove a geometric inequality involving w k (θ ) and the area A enclosed by the curve.As a by-product, we give a new proof of the classical isoperimetric inequality.Finally, we give some properties of convex curves with w k (θ ) being constant and pose an open problem motivated by the elegant Blaschke-Lebesgue theorem.

Locations

Pacific Journal of Mathematics - View - PDF

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