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A positive solution to the Busemann-Petty problem in \(\mathbb{R}^4\). (English) Zbl 0937.52004
The author presents the solution to the Busemann-Petty problem in \(\mathbb R^4.\) One of the key ideas in the proof, previously employed by R. J. Gardner [Ann. Math., II. Ser. 140, No. 2, 435-447 (1994; Zbl 0826.52010)], is the use of cylindrical coordinates in computing the inverse spherical Radon transform.

MSC:
52A20 Convex sets in \(n\) dimensions (including convex hypersurfaces)
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