Bonnesen-style symmetric mixed inequalities. (English) Zbl 1347.52003
Summary: 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.
MSC:
| 52A10 | Convex sets in \(2\) dimensions (including convex curves) |
| 52A22 | Random convex sets and integral geometry (aspects of convex geometry) |
Keywords:
isoperimetric inequality; symmetric mixed isoperimetric deficit; symmetric mixed isoperimetric inequality; Bonnesen-style symmetric mixed inequalityReferences:
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