Recently, Lutwak, Yang and Zhang posed the notion of Lp-projection body and established the Lp-analog of the Petty projection inequality. In this paper, the notion of Lp-mixed projection body is introduced--the Lp-pro...Recently, Lutwak, Yang and Zhang posed the notion of Lp-projection body and established the Lp-analog of the Petty projection inequality. In this paper, the notion of Lp-mixed projection body is introduced--the Lp-projection body being a special case. The Petty projection inequality, as well as Lutwak＇s quermassintegrals （Lp-mixed quermassintegrals） extension of the Petty projection inequality, is established for Lp-mixed projection body.展开更多
Associated with the concepts of the Lp-mixed quermassintegrals, the Lp-mixed volume, and the Lp-dual mixed volume, we establish inequalities for the quermassintegrals of the Lp-projection body and the Lp-centroid body...Associated with the concepts of the Lp-mixed quermassintegrals, the Lp-mixed volume, and the Lp-dual mixed volume, we establish inequalities for the quermassintegrals of the Lp-projection body and the Lp-centroid body. Further, the general results for the Shephard problem of the Lp-projection body and the Lp-centroid body are obtained.展开更多
Lutwak showed the Busemann-Petty type problem(also called the Shephard type problem)for the centroid bodies.Grinberg and Zhang gave an affirmation and a negative form of the Busemann-Petty type problem for the L_(p)-c...Lutwak showed the Busemann-Petty type problem(also called the Shephard type problem)for the centroid bodies.Grinberg and Zhang gave an affirmation and a negative form of the Busemann-Petty type problem for the L_(p)-centroid bodies.In this paper,we obtain an affirmation form and two negative forms of the BusemannPetty type problem for the general L_(p)-centroid bodies.展开更多
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 established the Lp-petty projection inequality. In this paper, the several reverses of the Lp-petty projection inequality are shown.
Lutwak,Yang and Zhang defined the(p,q)-mixed volumes very recently.In this paper,some Brunn-Minkowski type inequalities on the(p,q)-mixed volumes are established based on the general Lp-projection bodies and the gener...Lutwak,Yang and Zhang defined the(p,q)-mixed volumes very recently.In this paper,some Brunn-Minkowski type inequalities on the(p,q)-mixed volumes are established based on the general Lp-projection bodies and the general Lp-centroid bodies.展开更多
In this paper, combining with the L_p-dual geominimal surface area and the general L_p-centroid bodies, we research the Shephard type problems for general L_p-centroid bodies.
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
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
基金Research supported in part by the Natural Science Foundation of China(Grant No.10671117)Academic Mainstay Foundation of Hubei Province of China(Grant No.2003A005)
文摘Recently, Lutwak, Yang and Zhang posed the notion of Lp-projection body and established the Lp-analog of the Petty projection inequality. In this paper, the notion of Lp-mixed projection body is introduced--the Lp-projection body being a special case. The Petty projection inequality, as well as Lutwak＇s quermassintegrals （Lp-mixed quermassintegrals） extension of the Petty projection inequality, is established for Lp-mixed projection body.
基金Sponsored by the Natural Science Foundation of China (10671117)Academic Mainstay Foundation of Hubei Province of China (D200729002)Science Foundation of China Three Gorges University
文摘Associated with the concepts of the Lp-mixed quermassintegrals, the Lp-mixed volume, and the Lp-dual mixed volume, we establish inequalities for the quermassintegrals of the Lp-projection body and the Lp-centroid body. Further, the general results for the Shephard problem of the Lp-projection body and the Lp-centroid body are obtained.
基金supported in part by the Natural Science Foundation of China (Grant No.11371224)。
文摘Lutwak showed the Busemann-Petty type problem(also called the Shephard type problem)for the centroid bodies.Grinberg and Zhang gave an affirmation and a negative form of the Busemann-Petty type problem for the L_(p)-centroid bodies.In this paper,we obtain an affirmation form and two negative forms of the BusemannPetty type problem for the general L_(p)-centroid bodies.
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Foundation item： Supported by the Natural Science Foundation of China（10671117） Supported by Academic Mainstay Foundation of Hubei Province of China（D200729002） Supported by Science Foundation of China Three Gorges University
文摘Lutwak, Yang and Zhang established the Lp-petty projection inequality. In this paper, the several reverses of the Lp-petty projection inequality are shown.
基金Supported by the National Natural Science Foundation of China(11371224)Innovation Foundation of Graduate Student of China Three Gorges University(2019SSPY145)。
文摘Lutwak,Yang and Zhang defined the(p,q)-mixed volumes very recently.In this paper,some Brunn-Minkowski type inequalities on the(p,q)-mixed volumes are established based on the general Lp-projection bodies and the general Lp-centroid bodies.
文摘In this paper, combining with the L_p-dual geominimal surface area and the general L_p-centroid bodies, we research the Shephard type problems for general L_p-centroid bodies.
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(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.
