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J. Korean Math. Soc. 2011; 48(2): 421-430
Printed March 1, 2011
https://doi.org/10.4134/JKMS.2011.48.2.421
Copyright © The Korean Mathematical Society.
Some new Bonnesen-style inequalities
Jiazu Zhou, Yunwei Xia, and Chunna Zeng
Southwest University, Southwest University, Southwest University
By evaluating the containment measure of one domain to contain another, we will derive some new Bonnesen-type inequalities (Theorem 2) via the method of integral geometry. We obtain Ren's sufficient condition for one domain to contain another domain (Theorem 4). We also obtain some new geometric inequalities. Finally we give a simplified proof of the Bottema's result.
Keywords: the isoperimetric inequality, kinematic formula, containment measure, convex domain, the Bonnesen-style inequality
MSC numbers: Primary 52A22, 53C65; Secondary 51C16
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