A geometric proof of some inequalities involving mixed volumes
Using spherical harmonics, \textit{R. Schneider} [Mathematika 36, No. 1, 50-59 (1989; Zbl 0671.52008)] and \textit{P. R. Goodey} and \textit{H. Groemer} [Proc. Am. Math. Soc. 109, No. 4, 1103-1114 (1990; Zbl 0699.52001)] proved stability versions of special cases of the Alexandrov-Fenchel inequalities. Here a proof is given which uses the Blaschke-Santaló inequality and a variational argument instead of spherical harmonics.
scientific article; zbMATH DE number 1505607