Harmonic Maps and Rules of Symmetry (I)


Fang-Hua Lin

13:30:00 - 15:00:00

308 , Mathematics Research Center Building (ori. New Math. Bldg.)

After a brief general discussions on harmonic maps between two Riemannian manifolds, we should discuss in more details of harmonic maps into spheres. The idea is to see how symmetricity implies some useful algebriac structures of partial differential equations describing the harmonic maps. In particular we shall discuss Noether Currents, Hopf Differential Forms and Stress-Energy Tensors as well as Conservation lawas. One would see certain integrable structures in these problems with target manifolds possess certain symmetries(in particular homogeneous spaces and special Lie groups). One then discuss some consequences of analytical estimates(regularity theory, energy quantizations and concentration sets dynamics). The validity of many of these consequences for harmonic maps into a general compact Riemannian manifold remain to be challenging open problems.