A note on isoparametric polynomials

Abstract

We show that any homogeneous polynomial solution of |\nabla F(x)|^2=m^2|x|^(2m-2), m>1, is either a radially symmetric polynomial F(x)=\pm |x|^m (for even m's) or it is a composition of a Chebychev polynomial and a Cartan-Münzner polynomial.

6 pages

References in corpus (1)

• A generalization of Cartan's theorem on isoparametric cubics

Cited by in corpus (1)

• New explicit solutions to the $p$-Laplace equation based on isoparametric foliations