Nonexistence of Smooth Axially Symmetric Harmonic Maps from B3 into S2 (Journal of Partial Differential Equations, 2020)
Inspired by the construction of blow-up solutions of the heat flow of harmonic maps from D^2 into S^2 via maximum principle (Chang et al., J. Diff. Geom., 36, 1992, pp. 507-515.) we provide examples of nonexistence of smooth axially symmetric harmonic maps from B^3 into S^2 with smooth boundary maps of degree zero.
Keywords: Harmonic map; axially symmetry; non-existence