A positive solution to the Busemann-Petty problem in \(\mathbb{R}^4\). (English) Zbl 0937.52004

Zhang, Gaoyong

Ann. Math. (2) 149, No. 2, 535-543 (1999).

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.

Reviewer: Serguey M.Pokas (Odessa)

MSC:

52A20

Convex sets in \(n\) dimensions (including convex hypersurfaces)

Keywords:

convex body; star body; Busemann-Petty problem; intersection body; Fourier transform; inverse spherical Radon transform; convexity; parallel section; cylindrical coordinates

Citations:

Zbl 0826.52010