Gradient map of isoparametric polynomial and its application to Ginzburg-Landau system. (English) Zbl 1191.53038
This paper deals with some abstract properties of the gradient map of the isoparametric polynomial, which are illustrated with concrete applications to the study of the Ginzburg-Landau system arising in superconductivity theory. Throughout this paper, there are identified both isoparametric polynomials and isoparametric hypersurfaces with their congruences under isometries of the Euclidean space. In the main result of this paper, the gradient map of its isoparametric polynomial is calculated explicitly. As a direct consequence, the author computes the Brouwer degree of the gradient map. Applications to the symmetry of solutions to the Ginzburg-Landau system are also provided. The proofs mainly rely on topological arguments.
Reviewer: Vicenţiu D. Rădulescu (Craiova)
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