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Annals of Mathematics, II. Series Vol. 149, No. 2, pp. 535543 (1999) 

A positive solution to the BusemannPetty problem in $\bbfR^4$Gaoyong ZhangReview from Zentralblatt MATH: The author presents the solution to the BusemannPetty problem in $\Bbb R^4.$ One of the key ideas in the proof, previously employed by {\it R. J. Gardner} [Ann. Math., II. Ser. 140, No. 2, 435447 (1994; Zbl 0826.52010)], is the use of cylindrical coordinates in computing the inverse spherical Radon transform. Reviewed by Serguey M.Pokas Keywords: convex body; star body; BusemannPetty problem; intersection body; Fourier transform; inverse spherical Radon transform; convexity; parallel section; cylindrical coordinates Classification (MSC2000): 52A20 Full text of the article:
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