In this paper, we investigate the translative containment measure for a convex domain Ki to contain, or to be contained in the homothetic copy of another convex domain tKj(t ≥ 0). Via the formulas of translative Blaschke and Poincaré in integral formula, we obtain a Bonnesen-style symmetric mixed isohomothetic inequality. The Bonnesen-style symmetric mixed isohomothetic inequality obtained is known as Bonnesen-style inequality if one of the domains is a disc. As a direct consequence, we attain an inequality which strengthen the result proved by Bonnesen, Blaschké and Flanders. Furthermore, by the containment measure and Blaschke's rolling theorem, we obtain the reverse Bonnesen-style symmetric mixed isohomothetic inequalities. These inequalities are the analogues of the known Bottema's result in 1933.
Yuanyuan WANG
,
Xingxing WANG
,
Chunna ZENG
. ON BONNESEN-STYLE SYMMETRIC MIXED ISOHOMOTHETIC INEQUALITY IN R2[J]. Acta mathematica scientia, Series B, 2019
, 39(5)
: 1319
-1329
.
DOI: 10.1007/s10473-019-0510-1
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