An explicit counter-example for the shephard problem of convex bodies in ℝn

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.

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Bibliographic Details
Published in:Acta mathematica Sinica. English series 2015, Vol.31 (12), p.1941-1950
Main Authors: Xia, Yun Wei, Zeng, Chun Na
Format: Article
Language:English
Subjects:
Mathematics
Mathematics and Statistics
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Description
Summary: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.
ISSN:1439-8516
1439-7617
DOI:10.1007/s10114-015-4561-5