摘要
In this paper,we investigate the translative containment measure for a convex domain K_i to contain,or to be contained in the homothetic copy of another convex domain tK_j(t≥0).Via the formulas of translative Blaschke and Poincare 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,Blaschke 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.
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.
作者
Yuanyuan WANG
Xingxing WANG
Chunna ZENG
王媛媛;王星星;曾春娜(College of Science, Wuhan University of Science and Technology, Wuhan 430081, China;School of Mathematics and Statistics, Shanghai Lixin University of Accounting and Finance, Shanghai 201620, China;School of Mathematical Sciences, Chongqing Normal University, Chongqing 401331, China)
基金
supported in part by the National Natural Science Foundation of China(11801048)
the Natural Science Foundation Project of CSTC(cstc2017jcyjAX0022)
Innovation Support Program for Chongqing overseas Returnees(cx2018034)
