Modified Busemann-Petty problem on sections of convex bodies
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The Busemann-Petty problem asks whether convex origin-symmetric bodies in ℝ n with smaller central hyperplane sections necessarily have smallern-dimensional volume. It is known that the answer is affirmative ifn≤4 and negative ifn≥5. In this article we replace the assumptions of the original Busemann-Petty problem by certain conditions on the volumes of central hyperplane sections so that the answer becomes affirmative in all dimensions.
KeywordsConvex Body Fractional Derivative Homogeneous Function Positive Real Root Section Function
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