In this paper,by the theory of geometric inequalities,some new Bonnesenstyle isoperimetric inequalities of n-dimensional simplex are proved.In several cases,these inequalities imply characterizations of regular simplex.
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 Blaschk...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.展开更多
We investigate the isoperimetric deficit upper bound, that is, the reverse Bonnesen style inequality for the convex domain in a surface X2 of constant curvature ε via the containment measure of a convex domain to con...We investigate the isoperimetric deficit upper bound, that is, the reverse Bonnesen style inequality for the convex domain in a surface X2 of constant curvature ε via the containment measure of a convex domain to contain another convex domain in integral geometry. We obtain some reverse Bonnesen style inequalities that extend the known Bottema＇s result in the Euclidean plane E2.展开更多
We discuss the higher dimensional Bonnesen-style inequalities. Though there are many Bonnesen-style inequalities for domains in the Euclidean plane R2 few results for general domain in Rn （n ≥ 3） are known. The res...We discuss the higher dimensional Bonnesen-style inequalities. Though there are many Bonnesen-style inequalities for domains in the Euclidean plane R2 few results for general domain in Rn （n ≥ 3） are known. The results obtained in this paper are for general domains, convex or non-convex, in Rn.展开更多
基金The Doctoral Programs Foundation(20113401110009)of Education Ministry of ChinaUniversities Natural Science Foundation(KJ2016A310)of Anhui Province
文摘In this paper,by the theory of geometric inequalities,some new Bonnesenstyle isoperimetric inequalities of n-dimensional simplex are proved.In several cases,these inequalities imply characterizations of regular simplex.
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)
文摘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.
基金supported by National Natural Science Foundation of China (Grant Nos.10971167, 11271302 and 11101336)
文摘We investigate the isoperimetric deficit upper bound, that is, the reverse Bonnesen style inequality for the convex domain in a surface X2 of constant curvature ε via the containment measure of a convex domain to contain another convex domain in integral geometry. We obtain some reverse Bonnesen style inequalities that extend the known Bottema＇s result in the Euclidean plane E2.
基金supported by National Natural Science Foundation of China (Grant No. 10971167)
文摘We discuss the higher dimensional Bonnesen-style inequalities. Though there are many Bonnesen-style inequalities for domains in the Euclidean plane R2 few results for general domain in Rn （n ≥ 3） are known. The results obtained in this paper are for general domains, convex or non-convex, in Rn.
