几个关于极坐标的Bonnesen型不等式

SEVERAL BONNESEN-STYLE INEQUALITIES ABOUT POLAR COORDINATES

本文研究了平面上C^2闭凸曲线的极坐标形式{O;ρ(θ)}.运用Bonnesen不等式的推广形式[1,2],得到关于ρ及ρ_θ的一些积分形式的Bonnesen型不等式,使得我们很容易得到等周不等式取等时的条件.

In this paper,we study C2 convex closed plane curve inpolar coordinates{O;p(θ)}.By using the extended Bonnesen inequalities[1,2],we obtain some new Bonnesen-type inequalities about integration ofpandpθ,so that we can easily get the conditions under which equality in the isoperimetric inequality holds.