Isoparametric polynomials and sums of squares
Differential Geometry
2022-10-13 v2 Algebraic Geometry
Abstract
Hilbert's 17th problem asks that whether every nonnegative polynomial can be a sum of squares of rational functions. It has been answered affirmatively by Artin. However, the question as to whether a given nonnegative polynomial is a sum of squares of polynomials is still a central question in real algebraic geometry. In this paper, we solve this question completely for the nonnegative polynomials associated with isoparametric polynomials, initiated by E. Cartan, which define the focal submanifolds of the corresponding isoparametric hypersurfaces.
Keywords
Cite
@article{arxiv.1811.05587,
title = {Isoparametric polynomials and sums of squares},
author = {Jianquan Ge and Zizhou Tang},
journal= {arXiv preprint arXiv:1811.05587},
year = {2022}
}
Comments
37pages, accepted by International Mathematics Research Notices