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
Petty＇s conjectured projection inequality is a famous open problem in the theory of convex bodies. In this paper, it is shown that an inequality relating to Lp-version of the Petty＇s conjectured projection inequalit...Petty＇s conjectured projection inequality is a famous open problem in the theory of convex bodies. In this paper, it is shown that an inequality relating to Lp-version of the Petty＇s conjectured projection inequality is developed by using the notions of the Lp-mixed volume and the Lp-dual mixed volume, the relation of the Lp-projection body and the geometric body Г-pK, the Bourgain-Milman inequality and the Lp-Bnsemann-Petty inequality. In addition, for each origin-symmetric convex body, by applying the Jensen inequality and the monotonicity of the geometric body Г-pK, the reverses of Lp-version of the Petty＇s conjectured projection inequality and the Lp-Petty projection inequality are given, respectively.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.
In this article, we study the convex bodies associated with Lp-projections in the Brunn-Minkowski-Firey theory, and apply the Fourier analytic methods to prove the linear stability in the Shephard problem for Lp-proje...In this article, we study the convex bodies associated with Lp-projections in the Brunn-Minkowski-Firey theory, and apply the Fourier analytic methods to prove the linear stability in the Shephard problem for Lp-projections of convex bodies.展开更多
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
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
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Project supported by the National Natural Science Foundation of China(No.10671117)the Key Science Research Foundation of Education Department of Hubei Province of China(No.2003A005).
文摘Petty＇s conjectured projection inequality is a famous open problem in the theory of convex bodies. In this paper, it is shown that an inequality relating to Lp-version of the Petty＇s conjectured projection inequality is developed by using the notions of the Lp-mixed volume and the Lp-dual mixed volume, the relation of the Lp-projection body and the geometric body Г-pK, the Bourgain-Milman inequality and the Lp-Bnsemann-Petty inequality. In addition, for each origin-symmetric convex body, by applying the Jensen inequality and the monotonicity of the geometric body Г-pK, the reverses of Lp-version of the Petty＇s conjectured projection inequality and the Lp-Petty projection inequality are given, respectively.
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(11161019)
文摘In this article, we study the convex bodies associated with Lp-projections in the Brunn-Minkowski-Firey theory, and apply the Fourier analytic methods to prove the linear stability in the Shephard problem for Lp-projections of convex bodies.
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.
