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2 results on '"Bonnesen-style symmetric mixed inequality"'

1. Bonnesen-style symmetric mixed inequalities.

Author

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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2. Bonnesen-style symmetric mixed inequalities

Author

Miao Luo, Pengfu Wang, and Jiazu Zhou

Subjects
Pure mathematics, symmetric mixed isoperimetric deficit, lcsh:Mathematics, Applied Mathematics, 010102 general mathematics, Mathematical analysis, Kinematics, Bonnesen-style symmetric mixed inequality, isoperimetric inequality, lcsh:QA1-939, 01 natural sciences, Integral geometry, 010101 applied mathematics, symbols.namesake, symmetric mixed isoperimetric inequality, Euclidean geometry, Poincaré conjecture, symbols, Mathematics::Metric Geometry, Discrete Mathematics and Combinatorics, 0101 mathematics, Isoperimetric inequality, Analysis, Mathematics
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 Poincare 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.

Full Text
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