Modified Busemann-Petty problem on sections of convex bodies A.Koldobsky, V.Yaskin and M.Yaskina
نویسندگان
چکیده
The Busemann-Petty problem asks whether originsymmetric convex bodies in R with smaller central hyperplane sections necessarily have smaller n-dimensional volume. It is known that the answer is affirmative if n ≤ 4 and negative if n ≥ 5. In this article we modify the assumptions of the original Busemann-Petty problem to guarantee the affirmative answer in all dimensions.
منابع مشابه
Busemann - Petty problem on sections of convex bodies
The Busemann-Petty problem asks whether origin-symmetric convex bodies in R n with smaller central hyperplane sections necessarily have smaller n-dimensional volume. It is known that the answer is affirmative if n ≤ 4 and negative if n ≥ 5. In this article we modify the assumptions of the original Busemann-Petty problem to guarantee the affirmative answer in all dimensions.
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