Leading Coefficients and Extreme Points of Homogeneous Polynomials

Recently, H. Hakopian proved that the squares of a bivariate homogeneous polynomial and of its gradient have, in general, the same set of maximum points on the sphere. A generalization of this result mentioned can be gained by a method O. D. Kellogg used years ago in the estimate of some coefficient functionals. Date received: July 31, 1995. Date revised: May 14, 1996.