The planar Busemann-Petty centroid inequality and its stability
نویسندگان
چکیده
منابع مشابه
The L-busemann-petty Centroid Inequality
The ratio between the volume of the p-centroid body of a convex body K in Rn and the volume of K attains its minimum value if and only if K is an origin symmetric ellipsoid. This result, the Lp-Busemann-Petty centroid inequality, was recently proved by Lutwak, Yang and Zhang. In this paper we show that all the intrinsic volumes of the p-centroid body of K are convex functions of a time-like par...
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متن کاملThe Generalized Busemann-petty Problem with Weights
This question is known as the generalized Busemann-Petty problem. For i = n − 1, the problem was posed by Busemann and Petty [2] in 1956. It has a long history, and the answer is affirmative if and only if n ≤ 4; see [3], [8], [11]. For the generalized Busemann-Petty problem the following statements are known. If i = 2, n = 4, an affirmative answer follows from that in the case i = n − 1. If 3 ...
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ژورنال
عنوان ژورنال: Transactions of the American Mathematical Society
سال: 2015
ISSN: 0002-9947,1088-6850
DOI: 10.1090/tran/6503