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.
For p > 0, Lutwak, Yang and Zhang introduced the concept of L_p-polar projection body Γ_(-p)K of a convex body K in Rn. Let p ≥ 1 and K, L ? Rnbe two origin-symmetric convex bodies, we consider the question of wh...For p > 0, Lutwak, Yang and Zhang introduced the concept of L_p-polar projection body Γ_(-p)K of a convex body K in Rn. Let p ≥ 1 and K, L ? Rnbe two origin-symmetric convex bodies, we consider the question of whether Γ_(-p) K ? Γ_(-p) L implies ?_p(L) ≤ ?_p(K),where ?_p(K) denotes the L_p-affine surface area of K and K = Voln(K)^(-1/p) K. We prove a necessary and sufficient condition of an analog of the Shephard problem for the L_p-polar projection bodies.展开更多
The Blaschke-Minkowski homomorphisms was defined by Schuster.Recently,Wang extended its concept to Lp version.In this paper,we obtain affirmative and negative forms of the Shephard type problems for Lp geominimal surf...The Blaschke-Minkowski homomorphisms was defined by Schuster.Recently,Wang extended its concept to Lp version.In this paper,we obtain affirmative and negative forms of the Shephard type problems for Lp geominimal surface areas with respect to the Lp Blaschke-Minkowski homomorphisms.展开更多
In this paper, we develop a Fourier analytic approach to study the problem in the Brunn-Minkowski-Firey theory of convex bodies. We formulate and solve a quasi-Shephard＇s problem on projections of convex bodies.
Comparing the volume of the projection body of a double cone and that of the projection body of a ball,we give an explicit counter-example for the Shephard problem of convex bodies in R^n（n≥3）and an affirmative ans...Comparing the volume of the projection body of a double cone and that of the projection body of a ball,we give an explicit counter-example for the Shephard problem of convex bodies in R^n（n≥3）and an affirmative answer to the question of Zhang.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
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 the National Natural Science Foundation of China(11561020,11371224)Supported by the Science and Technology Plan of the Gansu Province(145RJZG227)
文摘For p > 0, Lutwak, Yang and Zhang introduced the concept of L_p-polar projection body Γ_(-p)K of a convex body K in Rn. Let p ≥ 1 and K, L ? Rnbe two origin-symmetric convex bodies, we consider the question of whether Γ_(-p) K ? Γ_(-p) L implies ?_p(L) ≤ ?_p(K),where ?_p(K) denotes the L_p-affine surface area of K and K = Voln(K)^(-1/p) K. We prove a necessary and sufficient condition of an analog of the Shephard problem for the L_p-polar projection bodies.
基金Supported by the National Natural Science Foundation of China(11371224)Innovation Foundation of Graduate Student of China Three Gorges University(2019SSPY144)。
文摘The Blaschke-Minkowski homomorphisms was defined by Schuster.Recently,Wang extended its concept to Lp version.In this paper,we obtain affirmative and negative forms of the Shephard type problems for Lp geominimal surface areas with respect to the Lp Blaschke-Minkowski homomorphisms.
基金Supported by the National Natural Science Foundation of China(11161019,11371224)
文摘In this paper, we develop a Fourier analytic approach to study the problem in the Brunn-Minkowski-Firey theory of convex bodies. We formulate and solve a quasi-Shephard＇s problem on projections of convex bodies.
基金Supported by National Science Foundation of China(Grant No.11326073)Fundamental Research Funds for the Central Universities(Grant Nos.XDJK2013C134,SWU113061)Natural Scinece Foundation Project of CQ CSTC(Grant No.cstc 2014jcyjA00019)
文摘Comparing the volume of the projection body of a double cone and that of the projection body of a ball,we give an explicit counter-example for the Shephard problem of convex bodies in R^n（n≥3）and an affirmative answer to the question of Zhang.
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.
