1. Bonnesen-style symmetric mixed inequalities.
- Author
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Wang, Pengfu, Luo, Miao, and Zhou, Jiazu
- Subjects
- *
ISOPERIMETRIC inequalities , *SYMMETRIC functions , *ISOPERIMETRICAL problems , *EUCLIDEAN geometry , *KINEMATIC geometry , *POINCARE conjecture - Abstract
In this paper, we investigate the symmetric mixed isoperimetric deficit $\Delta_{2}(K_{0},K_{1})$ of domains $K_{0}$ and $K_{1}$ in the Euclidean plane $\mathbb{R}^{2}$ . 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. [ABSTRACT FROM AUTHOR]
- Published
- 2016
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