## 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)

Zbl 0826.52010
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