On the isoperimetric deficit upper limit

摘要

In this paper, the reverse Bonnesen style inequalities for convex domain in the Euclidean plane $mathbb R^2$ are investigated. The Minkowski mixed convex set of two convex sets $K$ and $L$ is studied and some new geometric inequalities are obtained. From these inequalities obtained, some isoperimetric deficit upper limits, that is, the reverse Bonnesen style inequalities for convex domain $K$ are obtained. These isoperimetric deficit upper limits obtained are more fundamental than the known results of Bottema (cite{bottema}) and Pleijel (cite{pleijel}).