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This paper investigates continuity of the solution to the even logarithmic Minkowski problem in the plane. It is shown that the weak convergence of a sequence of cone-volume measures in R~2 implies the convergence of the sequence of the corresponding origin-symmetric convex bodies in the Hausdorff metric. 相似文献
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Science China Mathematics - The Busemann-Petty problem asks whether symmetric convex bodies in the Euclidean space ?nwith smaller central hyperplane sections necessarily have smaller volumes.... 相似文献
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Niufa FANG 《数学年刊B辑(英文版)》2023,44(3):465-480
For a positive integer s, the projection body of an s-concave function f : Rn →[0, +∞), a convex body in the (n + s)-dimensional Euclidean space Rn+s, is introduced.Associated inequalities for s-concave functions, such as, the functional isoperimetric inequality, the functional Petty projection inequality and the functional Loomis-Whitney inequality are obtained. 相似文献
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