The Busemann--Petty problem via spherical harmonics.
The Busemann-Petty problem asks whether inequalities between volumes of central hyperplane sections of centrally symmetric convex bodies in \(\mathbb{R}^n\) imply a corresponding inequality for the volumes of the bodies. The author gives a short new proof for the positive part \((n\leq 4)\) of the solution. This proof also employs the parallel section function, but avoids the use of intersection bodies. An essential tool are spherical harmonics and the Funk-Hecke theorem.
scientific article; zbMATH DE number 1957034
scientific article