this paper,we introduce the L_(p) Shephard problem on entropy of log-concave functions,a comparison problem:whether ∏_(p)f≤∏_(p)g implies that Ent(f)≥Ent(g),for 1≤p<n,and Ent(f)≤Ent(g),for n<p,where ∏_(p)...this paper,we introduce the L_(p) Shephard problem on entropy of log-concave functions,a comparison problem:whether ∏_(p)f≤∏_(p)g implies that Ent(f)≥Ent(g),for 1≤p<n,and Ent(f)≤Ent(g),for n<p,where ∏_(p)f is the L_(p) projection body of a log-concave function f.Our results give a partial answer to this problem.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, 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.
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.
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
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
基金The National Natural Science Foundation of China(11701373)The Shanghai Sailing Program(17YF1413800)。
文摘this paper,we introduce the L_(p) Shephard problem on entropy of log-concave functions,a comparison problem:whether ∏_(p)f≤∏_(p)g implies that Ent(f)≥Ent(g),for 1≤p<n,and Ent(f)≤Ent(g),for n<p,where ∏_(p)f is the L_(p) projection body of a log-concave function f.Our results give a partial answer to this problem.
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.
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(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 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 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.
