On the Isoperimetric Deficit Upper Limit

Abstract

Abstract. In this paper, the reverse Bonnesen style inequalities for convex domain in the Euclidean plane 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 ([5]) and Pleijel ([22]).

Bonnesen-style Wulff isoperimetric inequality

“…The reverse Bonnesen-style inequality ( 42 ) is obtained by Bokowski, Heil, Zhou, Ma and Xu ( cf. [ 4 , 27 ]).…”