In this paper, we study the characteristic properties for Lp-centroid bod- ies, and an improved version of Busemann-Petty problem for Lp-centroid bodies is obtained. In addition, using the definitions of Lp-pole curva...In this paper, we study the characteristic properties for Lp-centroid bod- ies, and an improved version of Busemann-Petty problem for Lp-centroid bodies is obtained. In addition, using the definitions of Lp-pole curvature image and Lp-affine surface area, a new proof of Busemann-Petty problem for Lp-centroid bodies is given.展开更多
Lutwak, Yang, and Zhang posed the notion of Lp-curvature images and established several Lp analogs of the affne isoperimetric inequality. In this article, the notion of Lp-mixed curvature images is introduced, Lp-curv...Lutwak, Yang, and Zhang posed the notion of Lp-curvature images and established several Lp analogs of the affne isoperimetric inequality. In this article, the notion of Lp-mixed curvature images is introduced, Lp-curvature images being a special case. The properties and Lp analogs of the affne isoperimetric inequality are established for Lp-mixed curvature images.展开更多
Based on the notion of the complex L_(p)centroid body,we establish Brunn-Minkowski type inequalities and monotonicity inequalities for complex L_(p)centroid bodies in this article.Moreover,we obtain the affirmative fo...Based on the notion of the complex L_(p)centroid body,we establish Brunn-Minkowski type inequalities and monotonicity inequalities for complex L_(p)centroid bodies in this article.Moreover,we obtain the affirmative form of Shephard type problem for the complex L_(p)centroid bodies and its negative form.展开更多
In this paper, Brunn-Minkowski inequality and Dresher-type inequality for mixed width-integrals of Firey＇s p-sum are established. Further, we present the Dresher-type inequalities for dual quermassintegrals of the po...In this paper, Brunn-Minkowski inequality and Dresher-type inequality for mixed width-integrals of Firey＇s p-sum are established. Further, we present the Dresher-type inequalities for dual quermassintegrals of the polar of Lp projection body and Lp centroid body, which in special cases yield some previous inequalities.展开更多
文摘In this paper, we study the characteristic properties for Lp-centroid bod- ies, and an improved version of Busemann-Petty problem for Lp-centroid bodies is obtained. In addition, using the definitions of Lp-pole curvature image and Lp-affine surface area, a new proof of Busemann-Petty problem for Lp-centroid bodies is given.
基金Supported by Innovation Program of Shanghai Municipal Education Commission (10YZ160)Science and Technology Commission Foundation of Shanghai (071605123)Science Foundation for the Excellent Youth Scholars of Shanghai
文摘Lutwak, Yang, and Zhang posed the notion of Lp-curvature images and established several Lp analogs of the affne isoperimetric inequality. In this article, the notion of Lp-mixed curvature images is introduced, Lp-curvature images being a special case. The properties and Lp analogs of the affne isoperimetric inequality are established for Lp-mixed curvature images.
基金Supported by the National Natural Science Foundation of China(11901346)
文摘Based on the notion of the complex L_(p)centroid body,we establish Brunn-Minkowski type inequalities and monotonicity inequalities for complex L_(p)centroid bodies in this article.Moreover,we obtain the affirmative form of Shephard type problem for the complex L_(p)centroid bodies and its negative form.
基金Supported by the National Natural Science Foundation of China(11371224)the Innovation Foundation of Graduate Student of China Three Gorges University(2014CX097)Excellent Foundation of Degree Dissertation of Master of China Three Gorges University(2015PY071)
文摘In this paper, Brunn-Minkowski inequality and Dresher-type inequality for mixed width-integrals of Firey＇s p-sum are established. Further, we present the Dresher-type inequalities for dual quermassintegrals of the polar of Lp projection body and Lp centroid body, which in special cases yield some previous inequalities.
