1. Bonnesen-style symmetric mixed inequalities
- Author
-
Pengfu Wang, Miao Luo, and Jiazu Zhou
- Subjects
isoperimetric inequality ,symmetric mixed isoperimetric deficit ,symmetric mixed isoperimetric inequality ,Bonnesen-style symmetric mixed inequality ,Mathematics ,QA1-939 - Abstract
Abstract In this paper, we investigate the symmetric mixed isoperimetric deficit Δ 2 ( K 0 , K 1 ) $\Delta_{2}(K_{0},K_{1})$ of domains K 0 $K_{0}$ and K 1 $K_{1}$ in the Euclidean plane R 2 $\mathbb{R}^{2}$ . Via the known kinematic formulae of Poincaré and Blaschke in integral geometry, we obtain some Bonnesen-style symmetric mixed inequalities. These new Bonnesen-style symmetric mixed inequalities are known as Bonnesen-style inequalities if one of the domains is a disc. Some inequalities obtained in this paper strengthen the known Bonnesen-style inequalities.
- Published
- 2016
- Full Text
- View/download PDF