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
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.
