Heat flow of equivariant harmonic maps from \(\mathbb{B}^ 3\) into \(\mathbb{C}\mathbb{P}^ 2\)
The author investigates the existence of equivariant harmonic maps from the three-dimensional unit ball \(\mathbb{B}^3\) to the complex projective plane \(\mathbb{C}\mathbb{P}^2\), using the heat flow for the evolution equation of harmonic maps. The author shows that for certain equivariant initial and boundary conditions, there exists a global solution to this heat equation, which subconverges to an equivariant harmonic map with prescribed boundary as \(t\to\infty\). Here the images of the maps considered are not confined to some convex ball in \(\mathbb{C}\mathbb{P}^2\) but can reach any possible range.
scientific article; zbMATH DE number 1025795