Harmonic self-maps of cohomogeneity one manifolds (Q2324851)

The authors investigate harmonic self-maps of cohomogeneity one manifolds. The main results include: (1) They develop the theory of equivariant harmonic self-maps of compact cohomogeneity one manifolds. (2) They construct new harmonic self-maps of the compact Lie groups \(\mathrm{SO}(4 + 2)\), \(l\geq 1\) with degree \(-3\), of \(\mathrm{SO}(8)\), \(\mathrm{SO}(14)\) and \(\mathrm{SO}(26)\) with degree \(-5\) each, of \(\mathrm{SO}(10)\) with degree \(-7\), and of \(\mathrm{SO}(14)\) with degree \(-11\) by exhibiting linear solutions to nonlinear singular boundary value problems.