Sections of convex bodies and splitting problem for selections
نویسندگان
چکیده
منابع مشابه
The Complex Busemann-petty Problem on Sections of Convex Bodies
The complex Busemann-Petty problem asks whether origin symmetric convex bodies in C with smaller central hyperplane sections necessarily have smaller volume. We prove that the answer is affirmative if n ≤ 3 and negative if n ≥ 4.
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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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ژورنال
عنوان ژورنال: Journal of Mathematical Analysis and Applications
سال: 2007
ISSN: 0022-247X
DOI: 10.1016/j.jmaa.2006.12.051